Let be a positive differentiable function on

Prove that exists and is non-zero for each x.

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- May 14th 2009, 02:41 AMfardeen_gen[SOLVED] Prove that limit exists and is non-zero for each x?
Let be a positive differentiable function on

Prove that exists and is non-zero for each x. - May 14th 2009, 02:57 AMjosipive
- May 14th 2009, 10:11 AMMoo
Then note that

So

And we know that

Hence

And thus the limit is - May 14th 2009, 12:31 PMpankaj
The limit is of the type

(Using L'Hospital's Rule)

=