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# Limit of a sequence

Let be a function such that and is differentiable at . Let us set

Evaluate the limit .

Solution

Since is differentiable at , there is some such that

and is of course continuous.

Thus,

Let . There exists such that which in return means that . Hence , for larger than it holds that

On the other hand , the sum is a Riemann sum and converges to .

In conclusion,

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