Find the limit (if it exists). $$\lim _ { x \rightarrow 36 ^ { - } } \frac { \sqrt { x } - 6 } { x - 36 }$$
A) 0
B) $- \frac { 1 } { 12 }$
C) $\frac { 1 } { 72 }$
D) $\frac { 1 } { 12 }$
E) Limit does not exist.

Question

Quizplus · Accepted Answer

We can simplify the expression as follows: 
$$\frac { \sqrt { x } - 6 } { x - 36 } = \frac { \sqrt { x } - 6 } { \left( \sqrt { x } - 6 \right) \left( \sqrt { x } + 6 \right) } = \frac { 1 } { \sqrt { x } + 6 }$$
As $x$ approaches 36 from the left ($x \rightarrow 36^{-}$), the denominator approaches 12, which means the limit is $\frac {1}{12}$. Therefore, the correct answer is D.

Find the Limit (If It Exists) lim⁡x→36−x−6x−36\lim _ { x \rightarrow 36 ^ { - } } \frac { \sqrt { x } - 6 } { x - 36 }x→36−lim​x−36x​−6​

Find the Limit (If It Exists) $\lim _ { x \rightarrow 36 ^ { - } } \frac { \sqrt { x } - 6 } { x - 36 }$