JEE Main 202117 Mar, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002Consider the function f : R →\to→ R defined by f(x)={(2−sin(1x))∣x∣,x≠0\hfill0, x=0\hfillf(x) = \left\{ \matrix{ \left( {2 - \sin \left( {{1 \over x}} \right)} \right)|x|,x \ne 0 \hfill \cr 0,\,\,x = 0 \hfill \cr} \right.f(x)={(2−sin(x1))∣x∣,x=0\hfill0,x=0\hfill. Then f is :AOption A. not monotonic on (−-−∞\infty∞, 0) and (0, ∞\infty∞)BOption B. monotonic on (0, ∞\infty∞) onlyCOption C. monotonic on (−-−∞\infty∞, 0) onlyDOption D. monotonic on (−-−∞\infty∞, 0) ∪\cup∪ (0, ∞\infty∞)CheckSkip · show solution
