# Homework Help: Need some clarification on this limit

1. Dec 16, 2005

### UrbanXrisis

I need some clarification on this limit:

lim n-->infinity of (2^n)/(n^4)

since the bottom of the function reaches infinity way faster than the top, why isnt the limit zero? my book says that it is infinity.

2. Dec 16, 2005

### Astronuc

Staff Emeritus
I believe the numerator goes to infinity faster.

Take n=100, the numberator is 2100 which would be 1625, while the denominator is 1004 = 108.

I believe by applying l'Hôpital's rule, differentiate the numerator and denominator four-fold, the denominator becomes 4!, while the numerator is still factor of 2n

3. Dec 16, 2005

### Tide

It might help to compare logarithms of the numerator and denominator.

4. Dec 17, 2005

### HallsofIvy

Because the top of the function reaches infinity way faster than the bottom!

(Even 1.00001^n eventually increases faster than n^10000.)