Mathematics

Problem

A function

g

is defined by

g(x)=\begin{cases}\dfrac{x^{2}-4}{x-2}, & x<2,\\[4pt] kx+1,&x>2.\end{cases}

A student generated the following table of values for

g

using only

x<2

$x$	$1.80$	$1.90$	$1.99$	$1.999$
$g(x)$	$3.80$	$3.90$	$3.99$	$3.999$

(a) Using the table, estimate

\displaystyle\lim_{x\to2^-}g(x)

. Give your answer correct to the nearest

0.01

. (b) Determine the value of

k

that makes

g

possess a limit at

x=2

. Show your work. (c) For that value of

k

, state the common limit

\displaystyle\lim_{x\to2}g(x)