Let f(x)= cases x^ 2 +a, & x<1 ax+1, & x 1 cases Which of the following statements…

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

Problem

Let

f(x)=\begin{cases} x^{2}+a, & x<1\\ ax+1, & x\ge 1 \end{cases}

Which of the following statements about the limit

\displaystyle\lim_{x\to 1}f(x)

is true? (a) The limit exists only if

a=0

. (b) The limit exists only if

a=1

. (c) The limit exists for every real value of

a

. (d) The limit never exists for any real value of

a