Question
Find the fourth Taylor polynomial of $f(x)=e^{-x / 2}$ at $x=0,$ and use it to estimate$e^{-0.1}$
Step 1
The first few derivatives are as follows: \begin{align*} f'(x) &= -\frac{1}{2}e^{-x/2}, \\ f''(x) &= \frac{1}{4}e^{-x/2}, \\ f'''(x) &= -\frac{1}{8}e^{-x/2}, \\ f''''(x) &= \frac{1}{16}e^{-x/2}. \end{align*} Show more…
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