Question

How do you take L'Hopitals rule of this??(PROBLEM IN REPLY)

Answer 1

Problem is attached.

Answer 2

I'm having a hard time taking the L'hopitals rule of that problem(Problem is attached in reply).

Answer 3

i can't read it. is there really a 1 in front?
anyway the idea is to take the log and then compute the limit

Answer 4

Ah I got it, the answer is 1/e.

Answer 5

looks like it says
\[\lim_{x\to \frac{\pi}{4}}\tan(x)^{\tan(2x)}\]

Answer 6

I don't know how to do it, this problem was so hard that someone asked him in class and he answered it

Answer 7

is that what it says?

Answer 8

yeah, with a 1 up front, but that doesnt count really.

Answer 9

take the log get
\[\tan(2x)\ln(\tan(x))\]

Answer 10

now you have something that looks like
\[\infty\times 0\] so the gimmick is to rewrite using the reciprocal so you get \(\frac{0}{0}\) or \(\frac{\infty}{\infty}\)

Answer 11

probably a good idea to use
\[\frac{\ln(\tan(x))}{\cot(2x)}\] and now you can use l'hopital

Answer 12

then whatever you get (apparently it is 2, i didn't do it) raise \(e\) to that power, because your first step was to take the log