Estimate the Limit by Graphing the Function for an Appropriate $\lim _ { x \rightarrow 2 } \frac { x + 2 } { x ^ { 2 } - 4 } = \lim _ { x \rightarrow 2 } \frac { 1 } { 2 x } = - \frac { 1 } { 4 }$

question 340

Essay

Estimate the limit by graphing the function for an appropriate domain. Confirm your estimate by using L'Hopital's rule.
Show each step of your calculation.
-Which one is correct, and which one is wrong? Give reasons for your answers.
(a) $\lim _ { x \rightarrow 2 } \frac { x + 2 } { x ^ { 2 } - 4 } = \lim _ { x \rightarrow 2 } \frac { 1 } { 2 x } = - \frac { 1 } { 4 }$
(b)
$\lim _ { x \rightarrow 2 } \frac { x + 2 } { x ^ { 2 } - 4 } = \frac { 0 } { - 8 } = 0$

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Definitions:

Lower Control Limit

The lower threshold in control charts beneath which the process variability is considered out of control or unusual.

In Control

A term referring to a process that is operating within its expected variability limits and is stable over time.

Stable

Referring to a condition or system that remains unchanged over time or is resistant to sudden change or deterioration.

Capable

Possessing the ability, fitness, or quality necessary to do or achieve a specified thing.