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lim(x to 0) ((1+logx-x)/(1-2x+x^(2)) is ...

`lim_(x to 0) ((1+logx-x)/(1-2x+x^(2))` is equal to

A

`1`

B

`-1`

C

0

D

`-(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(x to 1)(lim)(1+logx-x)/(1-2x+2x)`
`=underset(x to 1)/(lim)(0+(1)/(x)-1)/(0-2+2x)` (sing L'hospital's rule)
`=underset(xto1)(lim)(-1//x^(2))/(2)` (using L'hospital's rule)
`=-(1)/(2)`
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