JEE Main 2008Annual, Paper 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002Let f(x)={(x−1)sin1x−1if x≠10if x=1f\left( x \right) = \left\{ {\matrix{ {\left( {x - 1} \right)\sin {1 \over {x - 1}}} & {if\,x \ne 1} \cr 0 & {if\,x = 1} \cr } } \right.f(x)={(x−1)sinx−110ifx=1ifx=1 Then which one of the following is true?AOption A. fff is neither differentiable at x = 0 nor at x = 1BOption B. fff is differentiable at x = 0 and at x = 1COption C. fff is differentiable at x = 0 but not at x = 1DOption D. fff is differentiable at x = 1 but not at x = 0CheckSkip · show solution
