Thread: [SOLVED] Limit we've seen a number of times

I should just look this up, but I can't figure out how to do a search for it. It's cropped up a couple of times, but I don't recall the answer, much less how to find it.

Anyway, here it is

(I'm remembering something about taking the log of the limit perhaps?)

-Dan

1


I will try to remember how to get this!


A little later...

Rewrite this as:

e^(ln(n)/n)

Then use L'Hostpital on ln(n)/n.

Lim e^(1/n) = 1
n→∞

Originally Posted by spammanon

1


I will try to remember how to get this!


Rewrite this as:

e^(ln(n)/n)

Then use L'Hostpital on ln(n)/n.

Lim e^(1/n)
n→∞

Aaah! I'd forgotten about that little trick. Thank you. (Yay! I remembered the answer correctly!)

-Dan

Do it without L'Hopital.

.

But, for for all .

Thus, .

Thus, .

Now use the Squeeze Theorem.