# Solve this limit when x tends to +infinity

1. Nov 21, 2006

### mohlam12

any hints to solve this limit when x tends to +infinity is way very appreciated !!!!
PS: i should not use the hopital rule...
I tried to factorize the x from the nominator and denominator but couldnt get to any result... i tried some other things.. but still nothing.

$$\frac{x^{\frac{2}{3}} - 3^{x}}{x^{\frac{5}{2}} + 2^{x}}$$

thanks very much

2. Nov 21, 2006

### arildno

Rewrite this as:
$$(\frac{3}{2})^{x}\frac{(\frac{x^{\frac{2}{3}}}{3^{x}})-1}{(\frac{x^{\frac{5}{2}}}{2^{x}})+1}$$

3. Nov 23, 2006

### mohlam12

okay the limit of (3/2)^x is +infinity
but i have to show that the limit of $$\frac{x^{2/3}}{3^x}$$ is zero... how ?? maybe I have to show that it is smaller than a number, then the limit of that number should be zero... by the way, we havent studied exponentials yet..

PS: I think this should be moved to calculus and beyond ?

Last edited: Nov 23, 2006
4. Nov 23, 2006

### Office_Shredder

Staff Emeritus
the limit of $$\frac{x^{2/3}}{3^x}$$ goes to zero.

EDIT: Latex is so texy :rofl:

Last edited: Nov 23, 2006
5. Nov 23, 2006

### mohlam12

yes.. but it is an indeterminate form... how is it equal to zero