Assume that $f$ is a function with $|f^{(n)}(x)|15,$ for all $n$ and all real $x.$ Let $T_n(x)$ denote the Taylor polynomial of degree $n$ for $f(x)$ about the point $x=0.$

Use the calculator below to help you determine what the least integer $n$ for which you can be sure that $T_n(\frac{1}{2})$ approximates $f(\frac{1}{2})$ accurately to $3$ decimal places. NOTE

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Use the calculator below to help you determine what the least integer $n$ for which you can be sure that $T_n(1)$ approximates $f(1)$ accurately to $3$ decimal places.

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Use the calculator below to help you determine what the least integer $n$ for which you can be sure that $T_n(2)$ approximates $f(2)$ accurately to $3$ decimal places.

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