MHB Help with High-Power Limit Problem

[Yankel]

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]

What ideas have you had so far?

 

[Yankel]

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]

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