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Theory and ExamplesThe series converges to sin x for all
Chapter 10, Problem 55E(choose chapter or problem)
Problem 55E
Theory and Examples
The series
converges to sin x for all x.
a. Find the first six terms of a series for cos x. For what values of x should the series converge?
b. By replacing x by 2x in the series for sin x, find a series that converges to sin 2x for all x.
c. Using the result in part (a) and series multiplication, calculate the first six terms of a series for 2 sin x cos x. Compare your answer with the answer in part (b).
Questions & Answers
QUESTION:
Problem 55E
Theory and Examples
The series
converges to sin x for all x.
a. Find the first six terms of a series for cos x. For what values of x should the series converge?
b. By replacing x by 2x in the series for sin x, find a series that converges to sin 2x for all x.
c. Using the result in part (a) and series multiplication, calculate the first six terms of a series for 2 sin x cos x. Compare your answer with the answer in part (b).
ANSWER:
SOLUTION
Step 1 of 5
Here, we are given a series of that converges to
for all x.
We are asked to do the following.