limit, n->infty, (ln(n))^5 / sqrt(n); limit, n->infty, arctan(n); ...

[Zeus579]

Hi guys, can you help me with these questions please?

1. Find the limit of (ln n)^5/sqrt(n) as n goes to infinity.

2. Find the limit of arctan(n) as n goes to infinity.

3. Find the limit of tanh（n) as n goes to infinity.

Thanks in advance!!!

 

[Ishuda]

Hi guys, can you help me with these questions please. 1. Find the limit of (ln n)^5/sqrt(n) as n goes to infinity. 2. Find the limit of arctan(n) as n goes to infinity. 3. Find the limit of tanh（n) as n goes to infinity. Thanks in advance!!!

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

For question (2), is the range of arctan(n) restricted, i.e. to something like
\(\displaystyle -\frac{\pi}{2}\, \lt\, \theta\, \lt\, \frac{\pi}{2}\)?

 

[ksdhart]

For problem #1, I'd use L'Hopital's Rule. Have you learned that in your class yet? For problem #2, Ishuda's given you a very nice hint. For problem #3, are you familiar with the exponential form of the hyperbolic trig functions? That is to say, did you know that:

\(\displaystyle \displaystyle \tanh \left(n\right)=\frac{e^{2n}-1}{e^{2n}+1}\)

Perhaps you might find that form to take the limit of? Especially if you know L'Hopital's Rule.