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The value of lim(x to oo) ((x^(2)-2x+1)...

The value of `lim_(x to oo) ((x^(2)-2x+1)/(x^(2)-4x+2))` is

A

`e^(2)`

B

`e^(-2)`

C

`e^(6)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(x to oo)lim ((x^(2)-2x+1)/(x^(2)-4x+2))^(x)`
`underset(x to oo)lim (1+(2x-1)/(x^(2)-4x+2))^(x)`
`=e^(underset(x to oo)lim((x(2x-1))/(x^(2)-4x+2)))=e^(2)`
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