Exam 3 Solutions Sp10

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

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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....
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