I decided to put my attempt at a solution before the question, because the "solution" is what my question is about.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Find the rate of convergence for the following as n->infinity:

lim [sin(1/n^2)]

n->inf

Let f(n) = sin(1/n^2) for simplicity.

2. The attempt at a solution

I was searching through other forums and resources, and finally found a solution.

It said to use the Maclaurin Series (thus x0 = 0), but this would make every term

to look like:

f(0) + f'(0)*(n^1) + (1/2)*f''(0)*(n^2) + (1/4)*f'''(0)*(n^3) + ... + remainder

3. Relevant equations

How can we solve when 1/0 is undefined?

For example, in *every* term we have a sin(1/0^x) somewhere. This doesn't work, obviously.

This is solvable using the first few terms of the Maclaurin polynomial according to other sources, but I do not understand how. Did I overlook something? Or am I fundamentally misunderstanding the question?

Thanks!

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# Rate of Convergence for sin(1/x^2) with Maclaurin is undefined?

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