Consider the function f(x)= cases x^ 2 -9 10 - x+1 , & x<3, 5, & x 3

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

Problem

Consider the function

f(x)= \begin{cases} \frac{x^{2}-9}{\sqrt{10}-\sqrt{x+1}}, & x<3,\\ 5, & x\ge 3. \end{cases}

Determine

\displaystyle\lim_{x\to 3^-} f(x)

. (a)

0

(b)

-24

(c)

5

(d)

\displaystyle\frac{1}{\sqrt{10}-2}