Let h(x)= cases 9-x^ 2 , & x3

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

h(x)=\begin{cases}\sqrt{9-x^{2}}, & x<3,\\ mx-2, & x>3.\end{cases}

Numerical values of

h

for

x<3

are shown below.

$x$	$2.80$	$2.90$	$2.99$	$2.999$
$h(x)$	$1.0770$	$0.9110$	$0.1995$	$0.0632$

(a) Based on the data, estimate

\displaystyle\lim_{x\to3^-}h(x)

. (b) Determine the value of

m

that guarantees

h

has a limit at

x=3

. Clearly show algebraic steps. (c) For that value of

m

, state the value of

\displaystyle\lim_{x\to3}h(x)