Question

Let $f(x) = \begin{cases} \- 2 \sin x & \quad \text{if } x \leq - \frac{\pi}{2}\\\ A \ \sin x + B & \quad \text{if } - \frac{\pi}{2} < x < \frac{\pi}{2} \\\ \cos & \quad \text{if } x \leq \frac{\pi}{2} \end{cases}$ For what values of A and B, the function $f (x)$ is continuous throughout the real line ?

• A. A = 1, B = 1
• B. A = - 1, B = 1
• C. A = - 1, B = - 1
• D. A = 1, B = - 1

Answer 1

Answer: (B)

A = - 1, B = 1

Answer 2

Given,
$f(x)=\begin{cases}-2 \sin X, \text { if } x \leq-\frac{\pi}{2} \\ A \sin x +B, \text { if }-\frac{\pi}{2}