Question

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Answer 1

I think the answer is supposed to be zero but how I get there?

Answer 2

I took the deribative of the top and the bottom but I just ended up at (100n^99)/(e^n) and don't know where to go from here.

Answer 3

You should see a pattern in the derivatives.

Answer 4

you can do l'hospitals again

Answer 5

well nevermind kainui did it for you

Answer 6

You could have left it. Maybe it is hard for some people to reach that.

Answer 7

The point is, L'H rule says the limit of a ratio is the same as the limit of the ratio of their derivatives as well. So we can just see that eventually n^100 will eventually become a constant while the bottom will always be a function of n.

Answer 8

If it is hard for you to see the constant kainui got.
You can look at a an example with a lesser power

Answer 9

Like what would f^(4)(x) look like if we had f(x)=x^5

Answer 10

I kinda understand what kainui said

Answer 11

coolness

Answer 12

Sorry, I realized I wasn't being cryptic enough, so I went more cryptical. =P

Answer 13

So does the limit even exist?

Answer 14

\[\frac{ d^n }{ dx^n }(x^n)=n!\] just for fun

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Yeah, it even exists and it's even zero. @jennisicle

Answer 15

Ah, that's what I thought, thanks!