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If f(x)={((log(1+x)-log(1-x))/(x)"," , ...

If `f(x)={((log(1+x)-log(1-x))/(x)"," , "when " x ne 0),(3"," , "when " x = 0):}` is

A

continuous at x = 0.

B

discontinuous at x = 0, but on removable

C

discountinuous at at x = 0, but removable

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Given , `f(x) ={((log(1+x)-log(1-x))/(x)",", x ne 0),(3"," , x =0):}`
Now, `lim_(x to 0)f(x)=lim_(x to 0) (log(1+x)-log(1-x))/(x)`
`=lim_(x to 0) =((1)/(1+x)+(1)/(1-x))/(1)=lim_(x to 0) ((1)/(1)+(1)/(1))/(1)=2`
` and f(0)=3`
`therefore lim _(x to 0) f(x) ne f(0)`
Hence, f(x) is discontinuous at x = 0 and removable .
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