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If `f(x)=((1-tanx)/(1+sinx))^(cosec x)` is to be made continuous at `x=0,` then `f(0)` must be equal toA. `e^(2)`B. `e`C. `(I)/(e)`D. `(I)/(e^(2))` |
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Answer» Correct Answer - D If f (x) is continuous at x=0,` then underset(xrarr0)lim f (x) -f(0)` `impliesf (0) =underset(xrarr0)lim f (x) = e^(underset(srarr0)lim((-tanx-sin x)/((1-sin x).sin x)))` `= e^(underset(xrarr0)(lim)).((1+cos x))/((1-sin x),cos x)=e^(-2)` |
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