Estimate the Limit by Graphing the Function for an Appropriate $\lim _ { x \rightarrow 4 } \frac { x - 4 } { x ^ { 2 } - 4 } = \lim _ { x - 4 } \frac { 1 } { 2 x } = \frac { 1 } { 8 }$

question 264

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) $\lim _ { x \rightarrow 4 } \frac { x - 4 } { x ^ { 2 } - 4 } = \lim _ { x - 4 } \frac { 1 } { 2 x } = \frac { 1 } { 8 }$
(b) $\lim _ { x \rightarrow 4 x ^ { 2 } - 4 } \frac { x - 4 } { 12 } = \frac { 0 } { 12 } = 0$

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