Let f(x)= cases 3x+1 & x<2 kx^2-5 & x 2 cases Determine the value of that ensures is…

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

Problem

Let

f(x)=\begin{cases} 3x+1 & x<2 \\ kx^2-5 & x\ge 2 \end{cases}

Determine the value of

k

that ensures

f

is continuous at

x=2

. (a)

k=\dfrac{3}{4}

(b)

k=3

(c)

k=6

(d)

k=\dfrac{1}{2}