Please prove

lim x-> 0+ (ln cotx)/(e^csc(^2)x) = 0 using L'Hopital's Rule.

Thanks!

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- July 28th 2009, 06:02 PMriceyL'Hopital's Rule
Please prove

lim x-> 0+ (ln cotx)/(e^csc(^2)x) = 0 using L'Hopital's Rule.

Thanks! - July 28th 2009, 06:22 PMProve It
This is tough, but not impossible.

We first need to check that this is of indeterminate form.

It is, since the top and the bottom .

So we need to take the derivative of the top and the derivative of the bottom.

.

So

As .

So the bottom .

Therefore this whole limit tends to . - July 28th 2009, 06:37 PMricey
would deriv of ln cot x be sinx/[(cosx )(-sin ^(2)x]

= 1/ [(-cosx) (sinx)] - July 28th 2009, 06:40 PMProve It
- July 28th 2009, 06:40 PMricey
okay phew lol