Limit of a composite function

I don't want an easy answer to this problem. However, I would be happy if you could provide me with theorems and/or techniques required to solve it.

I know that But the natural logarithm is in the way and I think that you can't calculate the limit IN the logarithm first.

Thanks in advance :)

P.S. Oh, and by the way could anyone recommend a book on calculus with challenging problems, because most of the usual calculus textbooks aren't rigorous enough for my college course. (My lecturer always finds a way to give much more complicated problems than those in textbooks)

Re: Limit of a composite function

Hello, Doubled144314!

We need these two theorems:

. .

. .

We have: .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

Re: Limit of a composite function

Quote:

Originally Posted by

**Doubled144314** I don't want an easy answer to this problem. However, I would be happy if you could provide me with theorems and/or techniques required to solve it.

I know that

But the natural logarithm is in the way and I think that you can't calculate the limit IN the logarithm first.

Thanks in advance :)

P.S. Oh, and by the way could anyone recommend a book on calculus with challenging problems, because most of the usual calculus textbooks aren't rigorous enough for my college course. (My lecturer always finds a way to give much more complicated problems than those in textbooks)

I would rewrite the function as , and since this goes to you can apply L'Hospital's Rule.