Let . If is continuous on , then find the values of and…

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

f(x) = \begin{cases} -2\sin x, & \text{for } -\pi \le x \le -\frac{\pi}{2} \\ a \sin x + b, & \text{for } -\frac{\pi}{2} < x < \frac{\pi}{2} \\ \cos x, & \text{for } \frac{\pi}{2} \le x \le \pi \end{cases}

. If

f

is continuous on

[-\pi, \pi]

, then find the values of

a

and

b

.

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