Question

If $f\left(x\right)-\{\begin{array}{cc}xsinx,& when0<x\le \frac{\pi }{2}\\ \frac{\pi }{2}sin(\pi +x),& when\frac{\pi }{2}<x<\pi \end{array}$ , then

• A. f(x) is discontinuous at $x=\frac{\pi }{2}$
• B. f(x) is continuous at $x=\frac{\pi }{2}$
• C. f(x) is continuous at x = 0
• D. None of these

Answer 1

The correct option is A f(x) is discontinuous at $x=\frac{\pi }{2}$

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