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   "source": [
    "## Homework Problem: Taylor Series e^x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import factorial\n",
    "factorial(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "factorial(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create the taylor series for e^x and keep running the series until the error is less than 0.001 compared to Python's math.exp() function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter a number between 0 and 10: -1\n",
      "Enter a number between 0 and 10: 12\n",
      "Enter a number between 0 and 10: 2\n",
      "approximation: 7.3887125220458545\n",
      "using math.exp(): 7.38905609893065\n",
      "error: 0.0003435768847959153\n",
      "The loop ran 11 times\n"
     ]
    }
   ],
   "source": [
    "from math import factorial, exp\n",
    "\n",
    "# validate user input, make them enter a number between 0 and 10\n",
    "\n",
    "# set input as invalid\n",
    "x = -1\n",
    "\n",
    "# while not (what you want):\n",
    "while not (x>=0 and x<=10):\n",
    "    # ask for input\n",
    "    x_str = input('Enter a number between 0 and 10: ')\n",
    "    # run any code on the input\n",
    "    x = float(x_str)\n",
    "    \n",
    "approx = 0\n",
    "i=0\n",
    "while not (abs(exp(x)-approx)<0.001):\n",
    "    try:\n",
    "        term = (x**i)/(factorial(i))\n",
    "    except:\n",
    "        break\n",
    "    approx = approx + term\n",
    "    i = i + 1\n",
    "\n",
    "print(f'approximation: {approx}')\n",
    "print(f'using math.exp(): {exp(x)}')\n",
    "print(f'error: {abs(exp(x)-approx)}')\n",
    "print(f'The loop ran {i+1} times')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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