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    "# Exercises on Root-finding Without Derivatives"
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    "## Exercise 1: Comparing Root-finding Methods\n",
    "\n",
    "**Note:** This builds on the previous exercise comparing the Bisection and Newton's Methods;\n",
    "just adding the Secant Method.\n",
    "\n",
    "A) Write a Python function implementing the secant method with usage\n",
    "\n",
    "    (root, errorEstimate, iterations, functionEvaluations) = secant(f, a, b, errorTolerance, maxIterations)\n",
    "\n",
    "Update your previous implementations of the bisection method and Newton's method to mimic this interfacce:\n",
    "\n",
    "    (root, errorEstimate, iterations, functionEvaluations) = bisection(f, a, b, errorTolerance, maxIterations)\n",
    "    \n",
    "    (root, errorEstimate, iterations, functionEvaluations) = newton(f, x_0, errorTolerance, maxIterations)\n",
    "\n",
    "**Aside:** the last parameter `maxIterations` could be optional, with a default like `maxIterations=100`.\n",
    "\n",
    "B) Use these to solve the equation\n",
    "\n",
    "$$ 10 - 2x + \\sin(x) = 0 $$\n",
    "\n",
    "i) with [estimated] absolute error of no more than $10^{-8}$, and then\n",
    "\n",
    "ii) with [estimated] absolute error of no more than $10^{-15}$.\n",
    "\n",
    "Note in particular how many iterations and how many function evaluations are needed.\n",
    "\n",
    "C) Discuss: rank these methods for speed, as indicated by these experiments, and explain your ranking."
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    "---\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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