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   "source": [
    "# Exercises on Newton's Method"
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   "source": [
    "## Exercise 1\n",
    "\n",
    "a) Show that Newton's method applied to\n",
    "\n",
    "$$ f(x) = x^k - a $$\n",
    "\n",
    "leads to fixed point iteration with function\n",
    "\n",
    "$$ g(x) = \\frac{(k-1) x + \\displaystyle \\frac{a}{x^{k-1}}}{k}. $$\n",
    "\n",
    "b) Then verify mathematically that the iteration\n",
    "$x_{k+1} = g(x_k)$ has super-linear convergence."
   ]
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   "source": [
    "---\n",
    "This work is licensed under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/)"
   ]
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