Mathematics

Problem

A function

f

is defined for all real numbers except possibly at

x=2

. Selected function values are shown below.

$x$	$1.7$	$1.8$	$1.9$	$1.95$	$2.05$	$2.1$	$2.2$	$2.3$
$f(x)$	$4.68$	$4.79$	$4.90$	$4.94$	$5.07$	$5.11$	$5.22$	$5.33$

Use the numerical information in the table to analyze the behavior of

f

near

x=2

. (a) Describe how the values of

f(x)

change as

x

approaches

2

from the left. (b) Describe how the values of

f(x)

change as

x

approaches

2

from the right. (c) Based on the trends you identified in parts (a) and (b), explain whether each one-sided limit exists and whether the two-sided limit

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

exists. Justify your conclusion with specific references to the data.

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