Let f(x)= cases c x, & x<0 d, & x=0 cx+d, & 0<x<2 x^ 2 -c, & x 2 cases For which…

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

Problem

Let

f(x)=\begin{cases} c\sin x, & x<0\\ d, & x=0\\ cx+d, & 0<x<2\\ x^{2}-c, & x\ge 2\end{cases}

For which ordered pair

(c,d)

f

continuous for all real numbers

x

? (a)

(1,1)

(b)

(2,0)

(c)

\left(\frac{4}{3},0\right)

(d)

(4,0)