use quarto, not Pluto to render pages

quarto/_freeze/derivatives/taylor_series_polynomials/execute-results/html.json

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+    "markdown": "# Taylor Polynomials and other Approximating Polynomials\n\n\n\nThis section uses these add-on packages:\n\n``` {.julia .cell-code}\nusing CalculusWithJulia\nusing Plots\nusing SymPy\nusing Unitful\n```\n\n\n\n\nThe tangent line was seen to be the \"best\" linear approximation to a function at a point $c$. Approximating a function by a linear function gives an easier to use approximation at the expense of accuracy. It suggests a tradeoff between ease and accuracy. Is there a way to gain more accuracy at the expense of ease?\n\n\nQuadratic functions are still fairly easy to work with. Is it possible to find the best \"quadratic\" approximation to a function at a point $c$.\n\n\nMore generally, for a given $n$, what would be the best polynomial of degree $n$ to approximate $f(x)$ at $c$?\n\n\nWe will see in this section how the Taylor polynomial answers these questions, and is the appropriate generalization of the tangent line approximation.\n\n::: {.cell cache='true' hold='true' execution_count=4}\n\n::: {.cell-output .cell-output-display execution_count=5}\n```{=html}\n<div class=\"d-flex justify-content-center\">  <figure>  <img src=\"data:image/gif;base64,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 truncated
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