The table below lists selected values of a function for near

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

Problem

The table below lists selected values of a function

g

for

x

near

2

. The

x

–values are chosen so that the approach to

x=2

alternates on either side of 2.

$x$	1.9	1.99	1.999	2.001	2.01	2.1
$g(x)$	3.8	3.98	3.998	4.502	4.51	4.6

For the function

g

and the data provided: (a) Describe the numerical trend of

g(x)

x

approaches

2

from the left and from the right, citing specific evidence from the table. (b) Determine whether

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

exists. Justify your conclusion using precise limit language that references one–sided behavior. (c) Formally state the condition on one–sided limits that must be satisfied for

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

to exist, and explain which portion of that condition fails in this situation.

Related theory

Limits
Existence of a limit
Limits and Derivatives
Limits and Continuity

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