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lim(x->oo) ((x^2-2x+1)/(x^2-4x+2))^x is ...

`lim_(x->oo) ((x^2-2x+1)/(x^2-4x+2))^x` is equal to

A

`e^(2)`

B

`e^(-2)`

C

`e^(6)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`lim_(x to oo)((x^(2)-2x+1)/(x^(2)-4x+2))^(x)=lim_(x to oo)(1+(2x-1)/(x^(2)-4x+2))^(x)`
`=e^(lim_(x to oo)[(x(2x-1))/(x^(2)-4x+2)])=e^(2)`
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