Exam 3 Solutions Sp10

And for x 3 we have the series this is the opposite

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: for x = 3, we have the series This is the opposite of the alternating harmonic series, which converges. . So the convergence set is the half-closed interval (1, 3]. 11. Find the Maclaurin series for sin x + cos x. These two series are known, so all I need to do is to add them term by term. Here's what I get. 12. Find the first four nonzero terms in the power series based at a = 0 for the function multiplying might be easier than dividing.] For these two functions we have the series . [Hint: , which converges for all x, and , which converges for –1 < x < 1. Multiplying these gives 13. Find the Maclaurin polynomial of order three for the function y = sinh x. Then give a bound for the error in using P3(1) to estimate sinh(1). To investigate error, I'll need the fourth derivative anyway, so I'll make a table. n 0 sinh x 0 1 cosh x 1 2 sinh x 0 1 3 cosh x /6 4 sinh x So the third-order Maclaurin polynomial for y = sinh x is P3(1) for sinh(1) is exactly equal to This is bounded by sinh(1)/24. And the error involved in using , for some c between zero and 1....
View Full Document

This document was uploaded on 03/18/2014 for the course MATH 237 at Frostburg.

Ask a homework question - tutors are online