Problem 47E

Estimating errors Use the remainder term to estimate the absolute error in approximating the following quantities with the nth-order Taylor polynomial centered at 0. Estimates are not unique.

sin 0.3; n = 4

Solution 47E

Step 1

In this problem we have to find the absolute error using remainder term in approximating with the -order Taylor polynomial centered at 0.

Let us first find the order Taylor polynomial of sin x centered at 0.

Taylor series is given by .

In our case

So, what we need to do to get desired polynomial is to calculate derivatives, evaluate them at the given point and plug results into given formula.