{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import sympy\n",
    "from sympy import latex\n",
    "from IPython.display import HTML, display\n",
    "\n",
    "%matplotlib notebook\n",
    "\n",
    "sympy.init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# OMA 2. kolokvij 2013/2014"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. naloga"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Podana je funkcija $f(x)=x^2 e^{-x}$.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = sympy.symbols('x')\n",
    "f = lambda x: x**2 * sympy.E**(-x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Doloci definicijsko obmocje ${\\cal D}_f$ in izracunaj limiti v robovih ${\\cal D}_f$.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ker je eksponentna funkcija definirana povsod, je ${\\cal D}_f = \\mathbb{R}$.  \n",
    "$\\displaystyle{\\lim_{x\\to\\infty} x^2 e^{-x} = 0}.$  \n",
    "$\\displaystyle{\\lim_{x\\to -\\infty} x^2 e^{-x} = \\infty}.$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Poisci nicle in stacionarne tocke funkcije $f$.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFsAAAAUBAMAAAAQFlwTAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$x^{2} e^{- x} = 0$$"
      ],
      "text/plain": [
       " 2  -x    \n",
       "x ⋅ℯ   = 0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "equation = sympy.Eq(f(x), 0)\n",
    "equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "Nicle: $\\left [ 0\\right ]$"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solutions = sympy.solve(equation)\n",
    "s = 'Nicle: ${0}$'.format(latex(solutions))\n",
    "display(HTML(s))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALwAAAAWBAMAAACI4OsQAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEM3dMnarIkSJZlS7\nme8N5bApAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACTElEQVRIDa1UTWgTQRh9a3e7u000i0Ihh2iI\nnlSoWKQFDy6C5yZCRAuBtVq86YInL6YgPfSWokEUxIh4EQQ9ebCi3ntYoeLFguhJBY34W3qIk9n5\nZmd3E+lh5/K99773vWy+2QSIHfvd6xjPmNzEXMaJsbgpzPgxIVsyjeZCtomJtBeOKtiNE+dVPhS3\n1065Q5tK44iCgdpoeTomDCGGMzeyMKSnynagMrjbOjEOmOurbkJiVMf+lFi6fSOlPRJKbpWdV0Ah\nedPjsP+qUyt9I1voH1Xk+AB2JYetluXGfDMQPFcN9bPA15gjJHpXT6hj72GXE9rxZyvsSeQxu9fR\nChnFfwQuudJAoGkfsgmLmveQ+57QvvV6qqLNL50RH0fxE86g+PHT7WV1kOGCB2tTalr9wmI7ZFq7\n4UudAMUzfswR5mL9LbXTdU8A65eUi7hfPRyya74pNiK7QBRvbSA0W1O4ojj60K7wEzDYbEHfkO1l\n3HWecmZ+QcmVOoEofsRDaL76WFujdro2g378zsn+2QcHB4Vl9HP9XsLNHmrvh0rF4/I6hPnig1lx\nMQk7p/HlALQodicDjnx6o//Nufn3AFsksZhcdLXQf4pWIb141pHxz2H6oTnarAy1+S4mPSbkX2Is\nejGfGF3UuG0Hi6/KAQIUrwcw/ND8CTCona7sZ7W9TLK1me+aHc6MMko+6bJS/OVbd84J80lo/3kx\ncRS7XRrX5muNh4I0ZjskR5XiJ3q9H8JsvKGJyKagYn1r/+V8hOKV+Syhlt7XFuL/AXIHhKdfba95\nAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$- x^{2} e^{- x} + 2 x e^{- x} = 0$$"
      ],
      "text/plain": [
       "   2  -x        -x    \n",
       "- x ⋅ℯ   + 2⋅x⋅ℯ   = 0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "derivative = sympy.diff(f(x), x)\n",
    "equation = sympy.Eq(derivative, 0)\n",
    "equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "Stacionarne tocke: $\\left [ 0, \\quad 2\\right ]$"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solutions = sympy.solve(equation)\n",
    "s = 'Stacionarne tocke: ${0}$'.format(latex(solutions))\n",
    "display(HTML(s))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Narisi graf funkcije $f$.*    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7f58e38b07f0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.plotting.plot(f(x), (x, -1, 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. naloga"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Izracunaj nedoloceni integral racionalne funkcije \n",
    "$$\\int \\frac{x}{(x-1)(x-2)}.$$*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOAAAAAUBAMAAABmACzdAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n5QAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$2 \\log{\\left (x - 2 \\right )} - \\log{\\left (x - 1 \\right )}$$"
      ],
      "text/plain": [
       "2⋅log(x - 2) - log(x - 1)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = lambda x: x/((x-1)*(x-2))\n",
    "sympy.integrate(f(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Z integracijo po delih izracunaj\n",
    "$$\\int_{0}^{\\pi}x\\cos(x)dx.$$*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJsAAAAUBAMAAABoqVKyAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nOdQAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$x \\sin{\\left (x \\right )} + \\cos{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "x⋅sin(x) + cos(x)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = lambda x: x*sympy.cos(x)\n",
    "sympy.integrate(f(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. naloga"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Resi linearno diferencialno enacbo prvega reda\n",
    "$$ y' - \\frac{y}{x} = 2x^2.$$*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAM4AAAArBAMAAADCuKrGAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nn5p4Y35y4nsQk8V9b/qA7P/AeQ34oHeG+QAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\frac{d}{d x} f{\\left (x \\right )} - \\frac{1}{x} f{\\left (x \\right )} = 2 x^{2}$$"
      ],
      "text/plain": [
       "d          f(x)      2\n",
       "──(f(x)) - ──── = 2⋅x \n",
       "dx          x         "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = sympy.symbols('f', cls=sympy.Function)\n",
    "equation = sympy.Eq(f(x).diff(x)-f(x)/x, 2*x**2)\n",
    "equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKoAAAAcBAMAAAADyznZAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$f{\\left (x \\right )} = x \\left(C_{1} + x^{2}\\right)$$"
      ],
      "text/plain": [
       "         ⎛      2⎞\n",
       "f(x) = x⋅⎝C₁ + x ⎠"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solution = sympy.dsolve(equation, f(x))\n",
    "solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Upostevajmo se robni pogoj."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAF8AAAARBAMAAABJMG3aAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12\nVGZoascqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABO0lEQVQoFXVRv0vDQBh9KQkt0oPOLi0dCrp0\nEJyDf0FVcC6FOnSwRZCCDrq6uapDs+jgEnFw8IYGnJwK3dzyV1QRtH7f5ZpeL+kb8r0f38tdCJz6\njg8b3vvxiTOw3UQfofidST5iiK04Y+OzBXSBWzs5fCCnWUltESnqdfpUuAP6fholZEw+rpemLgAT\nCii0C4Vf3t1bUyA75BcaqAYs9pfOyglA6YujC8l4YXoZ8RNwn5MJq7DR1v5ihL5ibiPQjlWoazsd\nI3XFFoQqFKV8u5eyzTF/NMo1piZCFsLXBeYROwRVmMKpED9/Yjyyrf5AgfYCVoSVgltDmQsGqgMS\nZ+sKm8PTnrHMVPwBU7pt/gnj+fzHKuBgt3PFxUAHiys1Rq+xtnJHppC7ZZjiRgvP+khjx6TO9iwy\ndcL/AaPpUlWYczM4AAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$2 = C_{1} + 1$$"
      ],
      "text/plain": [
       "2 = C₁ + 1"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "equation = solution.subs(f(x), 2).subs(x, 1)\n",
    "equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAH0AAAAZBAMAAADuyzxaAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$f{\\left (x \\right )} = x^{3} + x$$"
      ],
      "text/plain": [
       "        3    \n",
       "f(x) = x  + x"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c1 = sympy.solve(equation)[0]\n",
    "C1 = sympy.symbols('C1')\n",
    "sympy.expand(solution.subs(C1, c1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. naloga"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Turist si v cerkvi ogleduje 3m visoko okno, ki se nahaja 1m nad njegovimi ocmi. Kako dalec od stene, na kateri se nahajo okno, naj se postavi, da bo razlika kotov pod katerimi vidi spodnji in zgornji kot okna najvecja?*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Najprej nastavimo enacbo. Kot, pod katerim iz razdalje $x$ vidimo spodnji del okna $\\arctan(\\frac{1}{x})$, zgorjnji del pa vidimo pod kotom $\\arctan(\\frac{4}{x})$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAN4AAAAyBAMAAADBz3h9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nyvY70TH5P7wcXvhGOlxeAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$- \\operatorname{atan}{\\left (\\frac{1}{x} \\right )} + \\operatorname{atan}{\\left (\\frac{4}{x} \\right )}$$"
      ],
      "text/plain": [
       "      ⎛1⎞       ⎛4⎞\n",
       "- atan⎜─⎟ + atan⎜─⎟\n",
       "      ⎝x⎠       ⎝x⎠"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = lambda x: sympy.atan(4/x) - sympy.atan(1/x)\n",
    "f(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kandidati za resitev so stacionarne tocke zgornje funkcije, torej nicle njenega odvoda. Pri tem dodatno zahtevamo, da so resitve pozitivne."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASQAAAA0BAMAAADRdljwAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nDzjfjAd8kRgrAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$- \\frac{4}{x^{2} \\left(1 + \\frac{16}{x^{2}}\\right)} + \\frac{1}{x^{2} \\left(1 + \\frac{1}{x^{2}}\\right)} = 0$$"
      ],
      "text/plain": [
       "       4             1         \n",
       "- ─────────── + ─────────── = 0\n",
       "   2 ⎛    16⎞    2 ⎛    1 ⎞    \n",
       "  x ⋅⎜1 + ──⎟   x ⋅⎜1 + ──⎟    \n",
       "     ⎜     2⎟      ⎜     2⎟    \n",
       "     ⎝    x ⎠      ⎝    x ⎠    "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sympy.symbols('x', positive=True)\n",
    "equation = sympy.Eq(f(x).diff(x), 0)\n",
    "\n",
    "equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABIAAAAUBAMAAAByuXB5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdt3NMolEIpm7EKvv\nVGZvmWXoAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAcklEQVQIHWMQMmEAgcdqDGEMDBWdUxiAdBgD\n1waG+AQwi3sBA88BMItHgYH7C5jF/AvGAupk+gUWA7LyA2AsbYgpDAwcDTCWBFAByGQG3gaGcgjL\ng4FBHMxiVw3tVgCzmP///w9hAZXDdOBhCamAJYXUAD28Hbf6IzqfAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left [ 2\\right ]$$"
      ],
      "text/plain": [
       "[2]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solutions = sympy.solve(equation)\n",
    "solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Postaviti se mora 2 metra od stene."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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   "file_extension": ".py",
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