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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^(1/x))`B. `f(x)="tan"^(-1) 1/x`C. `f(x)=(e^(1/x)-1)/(e^(1/x)+1)`D. `f(x)=(|sinx|)/(|x|)` |
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Answer» Correct Answer - D (A) `lim_(xrarr0^(-))f(x)=1 Lim_(xrarr0^(+))f(x)=0` (B) `Lim_(xrarr0^(+))f(x)=-(pi)/2 Lim_(xrarr0^(+))f(x)=(pi)/2` (C) `Lim_(xrarr0^(-))f(x)=-1 Lim_(xrarr0^(+))f(x)=1` `Lim_(xrarr0^(-))f(x)=Lim_(xrarr0^(+))f(x)=1` |
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