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Virtual Math Learning Center

Virtual Math Learning Center Texas A&M University Virtual Math Learning Center

Section 7.6 - The Taylor Approximation


Exercises

Directions: You should try to solve each problem first, and then click "Reveal Answer" to check your answer. You can click "Watch Video" if you need help with a problem.

1. Find the \(4^{\textrm{th}}\) degree Taylor polynomial, \(T_4(x)\), for \(\displaystyle f(x)=e^{-3x}-2-3x\) centered at \(x=4.\)

\(\begin{align}\displaystyle T_4(x)=&\left(e^{-12}-14\right)-\left(3e^{-12}+3\right)(x-4)+\frac{9}{2}e^{-12}(x-4)^2\\&-\frac{9}{2}e^{-12}(x-4)^3+\frac{27}{8}e^{-12}(x-4)^4\end{align}\)

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