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Evalaute lim(xto1) (1+logx-x)/(1-2x+x^(2...

Evalaute `lim_(xto1) (1+logx-x)/(1-2x+x^(2))`

A

0

B

1

C

`(1)/(3)`

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
`-1//2`
`underset(xto1)lim(1+logx-x)/(1-2x+x^(2))" "`(form 0/0)
`=underset(xto1)lim(0+(1)/(x)-1)/(0-2+2x)" "`(Using L'Hospital rule)
`=underset(xto1)lim(1-x)/(-2x(1-x))=underset(xto1)lim(1)/(-2x)=(-1)/(2)`
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