Question

If the function $f\left(x\right)=\{\begin{array}{cc}x+a^2\sqrt{2}sinx,& 0\le x<\frac{\pi }{4}\\ xcotx+b,& \frac{\pi }{4}\le x\le \frac{\pi }{2}\\ bsin2x-acos2x,& \frac{\pi }{2}<x\le \pi \end{array}$ is continuous in the interval $[0,\pi ]$ Then the values of (a, b) are
I. (-1, -1)
II. (0, 0)
III. (-1, 1)
IV. (1, 1)

• A. I and II are correct
• B. II and IV are correct
• C. III and IV are correct
• D. None of these

Answer 1

The correct option is B II and IV are correct

${lim}_{x\to \frac{{\pi }^{+}}{4}}f\left(x\right)={lim}_{x\to \frac{{\pi }^{-}}{4}}f\left(x\right)\Rightarrow a^2=b$
and ${lim}_{x\to \frac{{\pi }^{+}}{2}}f\left(x\right)={lim}_{x\to \frac{{\pi }^{-}}{4}}f\left(x\right)\Rightarrow a=b$