Evaluate the limit.

We use the definition of in terms of the exponential:

and the expansions (page 287 of Apostol) of and as :

Putting these together we evaluate 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 *(cosh x – cos x) / x*^{2}

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Evaluate the limit.

We use the definition of in terms of the exponential:

and the expansions (page 287 of Apostol) of and as :

Putting these together we evaluate the limit:

A bit confused about why we have 2cosx, when originally we start if with just cosx.

keep in mind that cosh(x) = 1/2 * (e^x + e^(-x)), he made a common denominator for cosh and cos