Find the limit $\lim _ { x \rightarrow 0 } \frac { \sqrt { x + 6 } - \sqrt { 6 } } { x }$, if it exists.
Select the correct answer.
A) Does not exist
B) $\frac { \sqrt { 6 } } { 12 }$
C) $\frac { \sqrt { 6 } } { 2 }$
D) $\frac { \sqrt { 6 } } { 6 }$

Question

Quizplus · Accepted Answer

The limit can be evaluated using L'Hopital's rule:$$\lim _ { x \rightarrow 0 } \frac { \sqrt { x + 6 } - \sqrt { 6 } } { x } = \lim _ { x \rightarrow 0 } \frac { \frac { 1 } { 2 \sqrt { x + 6 } } } { 1 } = \frac { 1 } { 2 \sqrt { 6 } } = \frac { \sqrt { 6 } } { 12 }$$

Find the Limit lim⁡x→0x+6−6x\lim _ { x \rightarrow 0 } \frac { \sqrt { x + 6 } - \sqrt { 6 } } { x }limx→0​xx+6​−6​​

Find the Limit $\lim _ { x \rightarrow 0 } \frac { \sqrt { x + 6 } - \sqrt { 6 } } { x }$