Evaluate the limit.

We know (page 287 of Apostol) that the expansions for and as are given by

Therefore, we have the following expansion for as ,

So, now we can take the limit,

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Stumbling Robot

A Fraction of a Dot
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Find the limit as *x* goes to 0 of *(cos (sin x) – cos x) / x*^{4}

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### Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):

Evaluate the limit.

We know (page 287 of Apostol) that the expansions for and as are given by

Therefore, we have the following expansion for as ,

So, now we can take the limit,

after “so now we can take the limit”

it’s -Cos x and not -sinx

that would change everything 😵