{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import sympy\n",
    "import numpy\n",
    "from sympy import Eq, solve\n",
    "from matplotlib import pyplot\n",
    "from sympy.mpmath import quad\n",
    "from math import log\n",
    "\n",
    "%matplotlib notebook\n",
    "\n",
    "def sample_function(f, start, end, step):\n",
    "    xs = numpy.linspace(start=start, stop=end, num=(end-start)/step)\n",
    "    ys = [f(x) for x in xs]\n",
    "    return xs, ys\n",
    "\n",
    "sympy.init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. kolokvij 2011/2012, rešitve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. naloga"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Poišči največjo in najmanjšo vrednost, ki jo zavzame funkcija \n",
    "$$f(x) = x^4 + 2x^3 - 2x^2 + 1.$$*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "f = lambda x: x**4 + 2*x**3 - 2*x**2 + 1\n",
    "x = sympy.Symbol('x', real=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kandadati za ekstreme so stacionarne točke in krajišči našega intervala. Stacionarne točke poiščemo z rešitvijo enačbe $f'(x)=0$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK0AAAAWBAMAAABAjAHGAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nxqoToaXqgYBvoPY/JCv9q8sfH32fXT3W9b8AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$4 x^{3} + 6 x^{2} - 4 x = 0$$"
      ],
      "text/plain": [
       "   3      2          \n",
       "4⋅x  + 6⋅x  - 4⋅x = 0"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq = Eq(f(x).diff(), 0)\n",
    "eq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHwAAAAyBAMAAABsYqKRAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n++wVy/rygHOUD93WOfS/4x7/kHv7HPgFOg1vyQmYfnIAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left [ -2, \\quad 0, \\quad \\frac{1}{2}\\right ]$$"
      ],
      "text/plain": [
       "[-2, 0, 1/2]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "critical_points = sympy.solve(eq)\n",
    "critical_points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAj4AAAAyBAMAAACuQczNAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left [ \\left ( -2, \\quad -7\\right ), \\quad \\left ( 0, \\quad 1\\right ), \\quad \\left ( \\frac{1}{2}, \\quad \\frac{13}{16}\\right ), \\quad \\left ( -3, \\quad 10\\right ), \\quad \\left ( 1, \\quad 2\\right )\\right ]$$"
      ],
      "text/plain": [
       "⎡                  ⎛     13⎞                  ⎤\n",
       "⎢(-2, -7), (0, 1), ⎜1/2, ──⎟, (-3, 10), (1, 2)⎥\n",
       "⎣                  ⎝     16⎠                  ⎦"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "end_points = [-3, 1]\n",
    "\n",
    "points = [(y, f(y)) for y in critical_points + end_points]\n",
    "points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO4AAAAUBAMAAAB4yRxuAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRK5CYII=\n",
      "text/latex": [
       "$$\\left ( \\left ( -2, \\quad -7\\right ), \\quad \\left ( -3, \\quad 10\\right )\\right )$$"
      ],
      "text/plain": [
       "((-2, -7), (-3, 10))"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(points, key=lambda point: point[1]), max(points, key=lambda point: point[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Določi tudi intervale naraščanja in padanja.*\n",
    "\n",
    "Funkcija narasca kjer je prvi odvod vecji od nic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVUAAAAyBAMAAAAepFVLAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left(-2 < x \\wedge x < 0\\right) \\vee \\left(\\frac{1}{2} < x \\wedge x < \\infty\\right)$$"
      ],
      "text/plain": [
       "(-2 < x ∧ x < 0) ∨ (1/2 < x ∧ x < ∞)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.solvers.reduce_inequalities([f(x).diff(x) > 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Funkcija pada, kjer je prvi odvod manjsi od nic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWUAAAAyBAMAAAB2V9dzAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nf145IhHQ8cjxHxf8UJM0xtizAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left(-\\infty < x \\wedge x < -2\\right) \\vee \\left(0 < x \\wedge x < \\frac{1}{2}\\right)$$"
      ],
      "text/plain": [
       "(-∞ < x ∧ x < -2) ∨ (0 < x ∧ x < 1/2)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.solvers.reduce_inequalities([f(x).diff(x) < 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. naloga"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Odpira se kavna hisa kava. Lastniki hise zelijo mesanico kave prodajati v licnih plocevinastih skatlicah, ki imajo obliko tristrane prizme s prostornino 1. Osnovna ploskev je enakostranicni trikotnik s stranico $a$, visina prizme je $b$. Pomagaj jim poiskati optimalno velikost skatlice: koliksna naj bosta $a$ in $b$, da bodo za izdelavo porabili cim manj plocevine?*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACcAAAAvBAMAAACS3s5rAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nSUVORK5CYII=\n",
      "text/latex": [
       "$$\\frac{2 \\sqrt{3}}{3 a^{2}}$$"
      ],
      "text/plain": [
       "    ___\n",
       "2⋅╲╱ 3 \n",
       "───────\n",
       "     2 \n",
       "  3⋅a  "
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = sympy.Symbol('a', real=True, positive=True)\n",
    "b = sympy.Symbol('b', real=True, positive=True)\n",
    "v = lambda a, b: a**2*b*sympy.sqrt(3)/2\n",
    "p = lambda a, b: a**2*sympy.sqrt(3) + 3*a*b\n",
    "b = solve(Eq(v(a,b), 1), b)[0]\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Izrazavo za $b$ vstavimo v enacbo za povrsino, jo odvajamo in poiscemo resitev enacbe $p'(a) = 0.$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGsAAAA/BAMAAAAVjiveAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nT0mE9rWGsyH+g1H7B5rf57o27PmcAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left ( 1, \\quad \\frac{2 \\sqrt{3}}{3}\\right )$$"
      ],
      "text/plain": [
       "⎛       ___⎞\n",
       "⎜   2⋅╲╱ 3 ⎟\n",
       "⎜1, ───────⎟\n",
       "⎝      3   ⎠"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val_a = sympy.solve(p(a, b).diff())[0]\n",
    "val_b = b.subs(a, val_a)\n",
    "val_a, val_b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. naloga"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Izracunaj nedolocena integrala\n",
    "$$\\int \\frac{(1+\\log(x))^2}{x}dx$$ \n",
    "in \n",
    "$$ \\int (x^2 -2)e^xdx .$$*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQIAAAAqBAMAAACq6UiMAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n9r5PUhXwL4f2OOoFaghqAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\frac{1}{3} \\log^{3}{\\left (x \\right )} + \\log^{2}{\\left (x \\right )} + \\log{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "   3                      \n",
       "log (x)      2            \n",
       "─────── + log (x) + log(x)\n",
       "   3                      "
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sympy.Symbol('x')\n",
    "f = lambda x: (1+sympy.log(x))**2/x\n",
    "g = lambda x: (x**2 - 2)*sympy.exp(x)\n",
    "sympy.integrate(f(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGsAAAAcBAMAAACUtlxGAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nLel6fSH2JuS5XYiiCPmv/+vIKrgDQ0h3p6+EKqcAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left(x^{2} - 2 x\\right) e^{x}$$"
      ],
      "text/plain": [
       "⎛ 2      ⎞  x\n",
       "⎝x  - 2⋅x⎠⋅ℯ "
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.integrate(g(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. naloga"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\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": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.ylim([-1, 5])\n",
    "pyplot.xlim([-1, 5])\n",
    "x = numpy.linspace(0, 2, 100)\n",
    "pyplot.plot([-1, 5], [0, 6], color='g')\n",
    "[xs, ys] = sample_function(lambda x: 2.0/x + 2, 0.01, 5, 0.01)\n",
    "pyplot.plot(xs, ys, color='r')\n",
    "pyplot.axvline(0, color='y')\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Presečišča na zgornji sliki se nahajajo pri $x_1=1$ in $x_2=2$.\n",
    "\n",
    "Ploščina lika je enaka $ \\log(4) - 0.5 $. Najlažje jo izračunamo tako, da lik razdelimo na dva dela glede na $x$-koordinato: na del med $0$ in $1$ in na del med $1$ in $2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. naloga"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Funkcija $F$ ima predpis\n",
    "$$F(x) = \\int_{-1}^x \\frac{\\log(1+t^2)}{t}dt.$$\n",
    "Poisci odvod funckcije $F$.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Njen odvod je kar enak funkciji pod integralom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHkAAAAqBAMAAABlzukjAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\frac{1}{x} \\log{\\left (x^{2} + 1 \\right )}$$"
      ],
      "text/plain": [
       "   ⎛ 2    ⎞\n",
       "log⎝x  + 1⎠\n",
       "───────────\n",
       "     x     "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sympy.Symbol('x', real=True)\n",
    "f = lambda x: sympy.log(1+x**2)/x\n",
    "F = lambda x: sympy.integrate(f(t), (t, -1, x))\n",
    "f(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Skiciraj graf odvoda $F'$ nato pa na isto sliko se graf $F$.*\n",
    "\n",
    "Z rdečo je narisan odvod, z zeleno pa graf funkcije $F$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlsAAAHfCAYAAABnDB0iAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe3acc79cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from math import log\n",
    "\n",
    "pylab.rcParams['figure.figsize'] = (10.0, 8.0)\n",
    "pylab.ylim([-1, 3])\n",
    "pylab.xlim([-4, 4])\n",
    "\n",
    "[xs, ys] = sample_function(f, -5, 5, 0.1)\n",
    "pyplot.plot(xs, ys, color='r')\n",
    "\n",
    "[xs, ys] = sample_function(lambda x: F(x), -5, 5, 0.2)\n",
    "pyplot.plot(xs, ys, color='g')\n",
    "pyplot.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}