1.

If both `Lim_(xrarrc^(-))f(x)` and `Lim_(xrarrc^(+))f(x)` exist finitely and are equal, then the function `f` is said to have removable discontinuity at `x=c`. If both the limits i.e. `Lim_(xrarrc^(-))f(x)` and `Lim_(xrarrc^(+))f(x)` exist finitely and are not equal, then the function `f` is said to have non-removable discontinuity at `x=c`. Which of the following function not defined at `x=0` has removable discontinuity at the origin?A. `f(x)=1/(1+2^(cotx))`B. `f(x)=xsin(pi)/x`C. `f(x)=1/(ln|x|)`D. `f(x)=sin((|sinx|)/x)`

Answer» Correct Answer - A::D
(A) `f(x)=1/(ln|x|) LHL=0= RHL`
(B)` f(x)=xsin(pi)/x LHL=0=RHL`
(C) `f(x)=1/(1+2^(cotx)) f(0)=` not define
`LHL=1`
`RHL=0impliesLHL!=RHL`
(D) `f(x)=sin((|sinx|)/x)LHL` (at `x=0`) `=sin(-1)=-sin1`
`RHL` (at` x=0`) `=sin1`
`LHL!=RHL`


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