Let F(x)= cases 1+cx -1 x , & x 0, [4pt] 2, & x=0

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

Problem

Let

F(x)= \begin{cases} \dfrac{\sqrt{1+cx}-1}{x}, & x\neq0,\\[4pt] 2, & x=0. \end{cases}

Find the value of the constant

c

so that

F

is continuous at

x=0

. (a)

c=2

(b)

c=1

(c)

c=4

(d)

c=6