l'hopital Question

**TeriyakiDonnQ** · May 9th 2010, 01:39 AM

Hiii :3

I'm stuck on this question:

lim (x->1) (2-x)^ tan(π/2)x

I did the ln thing but now i'm stuck what do I do next?
Plug it in?

Thank youuus :]

**Prove It** · May 9th 2010, 01:52 AM

Originally Posted by TeriyakiDonnQ

Hiii :3

I'm stuck on this question:

lim (x->1) (2-x)^ tan(π/2)x

I did the ln thing but now i'm stuck what do I do next?
Plug it in?

Thank youuus :]

Seeing as you've been told to use L'Hospital's Rule, it would make sense to use L'Hospital's Rule, wouldn't it?

You are correct that you should apply the exponential-logarithmic transformation...

$\lim_{x \to 1} (2 - x)^{\tan{\frac{\pi x}{2}}} = \lim_{x \to 1}e^{\ln{(2 - x)^{\tan{\frac{\pi x}{2}}}}}$

$= \lim_{x \to 1}e^{\tan{\left(\frac{\pi x}{2}\right)}\ln{(2 - x)}}$

$= \lim_{x \to 1}e^{\frac{\sin{\left(\frac{\pi x}{2}\right)}\ln{(2 - x)}}{\cos{\left(\frac{\pi x}{2}\right)}}}$

$= e^{\lim_{x \to 1}\frac{\sin{\left(\frac{\pi x}{2}\right)}\ln{(2 - x)}}{\cos{\left(\frac{\pi x}{2}\right)}}}$ .

This limit is now of the form $\frac{0}{0}$ , so now you can use L'Hospital's Rule.

Thread: l'hopital Question

LinkBack

Thread Tools

Display

l'hopital Question

Similar Math Help Forum Discussions

L hopital question

L'Hopital/limits question

L'Hopital's Rule question...

L'hopital question?

L'Hopital's rule question

Search Tags