Find the indicated limit if it exists. $\lim _ { x \rightarrow 4 } \frac { \sqrt { x } - 2 } { x - 4 }$
A) $\frac { 1 } { 4 }$
B) Does not exist
C) 4
D) $- \frac { 1 } { 4 }$

Question

Quizplus · Accepted Answer

The limit can be found by applying L'Hôpital's Rule, which is used when the direct substitution in the limit results in an indeterminate form like 0/0. Differentiating the numerator and the denominator separately with respect to x gives: $\lim _ { x \rightarrow 4 } \frac { \frac { 1 } { 2 \sqrt { x } } } { 1 } = \frac { 1 } { 2 \sqrt { 4 } } = \frac { 1 } { 4 }$.

Find the Indicated Limit If It Exists lim⁡x→4x−2x−4\lim _ { x \rightarrow 4 } \frac { \sqrt { x } - 2 } { x - 4 }limx→4​x−4x​−2​

Find the Indicated Limit If It Exists $\lim _ { x \rightarrow 4 } \frac { \sqrt { x } - 2 } { x - 4 }$