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

Question

Quizplus · Accepted Answer

This limit can be solved by applying the conjugate method. Multiply the numerator and denominator by the conjugate of the numerator, $\sqrt{x} + 2$, to get rid of the square root in the numerator. This simplifies to $\frac{1}{\sqrt{x} + 2}$ when $x \rightarrow 4$, which equals $\frac{1}{4}$.

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 $\lim _ { x \rightarrow 4 } \frac { \sqrt { x } - 2 } { x - 4 }$