The table gives values of a function for near

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

Problem

The table gives values of a function

g

for

x

near

5

. No value of

g

is provided at

x=5

$x$	$4.6$	$4.8$	$4.92$	$4.97$	$4.99$
$g(x)$	$12.41$	$12.90$	$12.98$	$12.995$	$12.999$

Assume

g

is defined for all

x<5

. (a) Estimate

\displaystyle \lim_{x\to 5^-} g(x)

to within

0.01

. (b) Provide a clear numerical justification that your estimate in part (a) is accurate to the stated tolerance.