(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the limit of [itex]n^2(e^\frac{1}{n^2} - cos(\frac{1}{n}))[/itex]

2. Relevant equations

3. The attempt at a solution

since cos(1/n) is asymptotic to 1. [itex]n^2(e^\frac{1}{n^2} - cos(\frac{1}{n}))[/itex] ~ [itex]n^2(e^\frac{1}{n^2} - 1)[/itex] ~ [itex]n^2 \frac{1}{n^2})[/itex] = 1

The right answer is 3/2 though. I don't see what's wrong with my reasoning. Maybe i used asymptotic in an illegitimate way. What's the problem?

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# Homework Help: Limit of sequence

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