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The value of underset(xrarr1)(lim)(root(...

The value of `underset(xrarr1)(lim)(root(13)x-root7x)/(root5x-root3x)` is

A

1

B

`-1`

C

0

D

`-1//2`

Text Solution

Verified by Experts

The correct Answer is:
D
Applying L'Hospital's rule,
`underset(xrarr1)(lim)(1+logx-x)/(1-2x+x^(2))=underset(xrarr1)(lim)((1)/(x)-1)/(-2+2x)=underset(xrarr1)(lim)(1-x)/(2x(x-1))`
`=underset(xrarr1)(lim)(-1)/(2x)=-(1)/(2)`
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