The table below lists computed values of a function for near

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

Problem

The table below lists computed values of a function

g

for

x

near

2

. Assume that

g

is defined for all

x\neq 2

$x$	1.8	1.9	1.95	1.99	2.01	2.05	2.1
$g(x)$	12.4	26.7	55.9	298.4	-312.7	-59.1	-28.3

Use the numerical evidence to analyze the behavior of

g

near

x=2

. (1) Determine

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

and

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

. Provide a brief verbal justification that cites specific trends in the table. (2) State the equation of any vertical asymptote suggested by the data and explain why the limit values you found support that conclusion. (3) Describe in words the overall one–sided behavior of the graph of

y=g(x)

near

x=2

. Include whether the function grows without bound positively or negatively on each side.

Related theory

Limits
Existence of a limit
Limits and Derivatives
Limits and Continuity

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