Evaluate lim 4^(n)(1-cos(theta/2^(n))) as n approaches infinity.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

Evaluate lim 4^(n)(1-cos(theta/2^(n))) as n approaches infinity.

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Follow-up Question

In step 2, how did you get the third part where it says limit 2^(n-1) x theta x sin(2^(-n)theta) as n approaches infinity.

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Follow-up Question

For the new solution problem at the bottom, how did you get (4^n/2^2n) = 1/4^n. Plus, why does (theta^(4)/4^n) times (1/4!) = 0?

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Follow-up Question

How infinity x 0 not zero? How come the final answer is infinity?

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How did you get the second step?

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