Write the remainder $R_{n}(x)$ in Lagrange form. $$f(x)=e^{-x}$$
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We can do this by using the formula: $$P_{n}(x)=\sum_{k=0}^{n}\frac{f^{(k)}(a)}{k!}(x-a)^{k}$$ where $f^{(k)}(x)$ denotes the $k$th derivative of $f(x)$. In this case, we have $a=0$ and $f(x)=e^{-x}$, so we can compute the derivatives as Show more…
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