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If lim(x to 0)(log(3+x)-log(3-x))/(x)=k,...

If `lim_(x to 0)(log(3+x)-log(3-x))/(x)=k`, then value of k is

A

0

B

`-(1)/(3)`

C

`(2)/(3)`

D

`-(2)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
Now, `underset(xto0)(lim)(log(3+x)-log(3-x))/(x)`
`=underset(xto0)(lim)((1)/(3+x)+(1)/(3-x))/(1)=(1)/(3)+(1)/(3)=(2)/(3)`
But `underset(xto0)(lim)(log(3+x)-log(3-x))/(x)=k`
`thereforek=(2)/(3)`
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