## jennisicle Group Title . 5 months ago 5 months ago

1. jennisicle Group Title

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

2. jennisicle Group Title

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.

3. myininaya Group Title

You should see a pattern in the derivatives.

4. myininaya Group Title

you can do l'hospitals again

5. myininaya Group Title

well nevermind kainui did it for you

6. myininaya Group Title

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

7. Kainui Group Title

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.

8. myininaya Group Title

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

9. myininaya Group Title

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

10. jennisicle Group Title

I kinda understand what kainui said

11. myininaya Group Title

coolness

12. Kainui Group Title

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

13. jennisicle Group Title

So does the limit even exist?

14. Kainui Group Title

$\frac{ d^n }{ dx^n }(x^n)=n!$ just for fun -- Yeah, it even exists and it's even zero. @jennisicle

15. jennisicle Group Title

Ah, that's what I thought, thanks!