1.

If f(x)=((1-tanx)/(1+sinx))^(cosec x) is to be made continuous at x=0, then f(0) must be equal to

Answer»

`e^(2)`
`e`
`(I)/(e)`
`(I)/(e^(2))`

SOLUTION :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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