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AP® Calculus AB-BC

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Moderate

Continuity of Piecewise Cosine Functions

APCALC-0NB5QF

Discuss the continuity of:
$$f(x)=\begin{Bmatrix} cos(x)\quad & x<-\pi \\\ |cos(x)| & -\pi \le x\le \frac { \pi }{ 2 } \\\ { cos }^{ 2 }(x) & x>\frac { \pi }{ 2 } \end{Bmatrix}$$

A

$f(x)$ is has a jump discontinuity at $x=\cfrac {\pi }{2}$.

B

$f(x)$ is continuous on $[-2\pi , 0]$.

C

$f(x)$ is continuous on $[-\pi , \pi ]$.

D

$f(x)$ is continuous for all real numbers.