Consider the function k(x)= cases x^ 2 -9 x-3 , & x3

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

Problem

Consider the function

k(x)= \begin{cases} \dfrac{x^{2}-9}{x-3}, & x<3,\\ \sqrt{x+6}-3, & x>3. \end{cases}

Which of the following statements is true about

\lim_{x\to3} k(x)

? (a) The limit exists and equals

6

. (b) The limit does not exist because the left-hand and right-hand limits are unequal. (c) The limit exists and equals

0

. (d) The limit does not exist because

k(3)

is undefined.