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\textbf{Math 126: Calculus II}
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\textbf{Quiz 9}\quad \textsl{November 16, 1999}

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Suppose you are required to use Taylor's formula to calculate $e^2$
with an error less than $10^{-10}$.
You know $e<3$, and you have the following information:
\def\t #1{10^{-#1}}
\def\a #1{\frac{2^{#1}}{#1\,!}}\def\b #1{\frac{9\cdot2^{#1}}{#1\,!}}
$$
\begin{array}{c}
\t9>\a{17}>\t{10}>\a{18}>\t{11}>\a{19}>\t{12}>\a{20}\\
\\
\t8>\b{17}>\t9>\b{18}>\t{10}>\b{19}>\t{11}>\b{20}
\end{array}
$$
What is the smallest number of terms (the smallest $n$)
to do the approximation ?
(This requires estimating the remainder.)
{\bf DO NOT} actually carry out the calculation of $e^2$.

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