Let f(x)= cases x-3,&x<0 ^2-3x+2,&x 0 cases and

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

f(x)=\begin{cases}x-3,&x<0\\x^2-3x+2,&x\geq 0\end{cases}

and

g(x)=f(|x|)+|f(x)|

. The value of

\lim_{x\to\frac{\pi}{2}} g(x)

is equal to (a)

\frac{\pi}{2}+1

(b)

\frac{\pi^2}{2}-3\pi+4

(c)

\frac{\pi^2}{2}+2\pi-3

(d) 0