Question

If $\sqrt{x}$ then

• A. $\sqrt{\sin\mspace{6mu} x}$ is discontinuous at $\sqrt{x}$
• B. $\sqrt{x}$ is continuous at $\left| \sin\frac{x}{2} \right| + \left| \cos x \right|$
• C. $\sqrt{\log_{\frac{1}{4}}\left( \frac{5x - x^{2}}{4} \right)} ⥄ ⥄$ is continuous at $f(x) = \left\{ \begin{matrix} \frac{2}{5 - x},\text{when}x < 3 \\ 5 - x,\text{when}x > 3 \end{matrix} \right.\$
• D. None of these

Answer 1

Answer: (A)

$\sqrt{\sin\mspace{6mu} x}$ is discontinuous at $\sqrt{x}$

Answer 2

$= \frac { \pi } { 2 } , \lim _ { x \rightarrow \frac { \pi ^ { + } } { 2 } } f ( x ) = - \frac { \pi } { 2 }$ and $f \left( \frac { \pi } { 2 } \right) = \frac { \pi } { 2 }$

Since $\lim _ { x + \frac { \pi ^ { - } } { 2 } } \neq \lim _ { x + \frac { \pi ^ { + } } { 2 } } f ( x )$ ,

$\therefore$ Function is discontinuous at $x = \frac { \pi } { 2 }$