# Limit with high powers

#### Yankel

##### Active member
hello,

I need some help with this limit...

$$\lim_{x\to \infty }\frac{(2x-1)^{10}(x-2)^{30}}{(x+1)^{20}(2x+3)^{20}}$$

thanks...

#### Ackbach

##### Indicium Physicus
Staff member
What ideas have you had so far?

#### Yankel

##### Active member
The only thing I could think of was to somehow push x^30 inside the powers, but I don't know how...

30 is the strongest power when it comes to infinity, so there must be something with 30.

#### CaptainBlack

##### Well-known member
hello,

I need some help with this limit...

$$\lim_{x\to \infty }\frac{(2x-1)^{10}(x-2)^{30}}{(x+1)^{20}(2x+3)^{20}}$$

thanks...

for $$x\ne 0$$ divide each of the 40 brackets at top and bottom by $$x$$:

$\frac{(2x-1)^{10}(x-2)^{30}}{(x+1)^{20}(2x+3)^{20}}= \frac{(2-x^{-1})^{10}(1-2x^{-1})^{30}}{(1+x^{-1})^{20}(2+3x^{-1})^{20}}$

CB