The function is defined for values of close to

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

Problem

The function

f

is defined for values of

x

close to

2

. Some of its values have been calculated and are shown below.

$x$	$1.7$	$1.8$	$1.9$	$1.95$	$1.99$	$2.01$	$2.05$	$2.10$	$2.20$	$2.30$
$f(x)$	$4.27$	$4.04$	$3.85$	$3.77$	$3.71$	$3.69$	$3.67$	$3.66$	$3.65$	$3.64$

Use the information in the table to answer the following. (i) Estimate

\displaystyle \lim_{x\to 2^-} f(x)

and

\displaystyle \lim_{x\to 2^+} f(x)

, correct to two decimal places. (ii) State, with reason, whether

\displaystyle \lim_{x\to 2} f(x)

exists. (iii) Interpret your result in part (ii) in the light of the intuitive idea of a limit.