jee-advanced 2011 Q49

jee-advanced · India · paper2 Curve Sketching Continuity and Discontinuity Analysis of Piecewise Functions

If $$f ( x ) = \begin{cases} - x - \frac { \pi } { 2 } , & x \leq - \frac { \pi } { 2 } \\ - \cos x , & - \frac { \pi } { 2 } < x \leq 0 \\ x - 1 , & 0 < x \leq 1 \\ \ln x , & x > 1 , \end{cases}$$ then
(A) $f ( x )$ is continuous at $x = -\frac{\pi}{2}$
(B) $f ( x )$ is not differentiable at $x = 0$
(C) $f ( x )$ is differentiable at $x = 1$
(D) $f ( x )$ is differentiable at $x = -\frac{3}{2}$

If
$$f ( x ) = \begin{cases} - x - \frac { \pi } { 2 } , & x \leq - \frac { \pi } { 2 } \\ - \cos x , & - \frac { \pi } { 2 } < x \leq 0 \\ x - 1 , & 0 < x \leq 1 \\ \ln x , & x > 1 , \end{cases}$$
then\\
(A) $f ( x )$ is continuous at $x = -\frac{\pi}{2}$\\
(B) $f ( x )$ is not differentiable at $x = 0$\\
(C) $f ( x )$ is differentiable at $x = 1$\\
(D) $f ( x )$ is differentiable at $x = -\frac{3}{2}$

Paper Questions

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