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