Evalue the limit.

First, we have

As we use the expansion for (page 287 of Apostol) to write,

From this we see that as ; and so,

Hence, using the expansion for as (page 287 of Apostol) we have

Therefore, we have

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Stumbling Robot

A Fraction of a Dot
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Find the limit as *x* goes to 0 of *((1+x)*^{1/x} – e) / x

Evalue the limit.

First, we have

As we use the expansion for (page 287 of Apostol) to write,

From this we see that as ; and so,

Hence, using the expansion for as (page 287 of Apostol) we have

Therefore, we have