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Limit with high powers

Yankel

Active member
Jan 27, 2012
398
hello,

I need some help with this limit...

[tex]\lim_{x\to \infty }\frac{(2x-1)^{10}(x-2)^{30}}{(x+1)^{20}(2x+3)^{20}}[/tex]

thanks...
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,197
What ideas have you had so far?
 

Yankel

Active member
Jan 27, 2012
398
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
Jan 26, 2012
890
hello,

I need some help with this limit...

[tex]\lim_{x\to \infty }\frac{(2x-1)^{10}(x-2)^{30}}{(x+1)^{20}(2x+3)^{20}}[/tex]

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