Find the limit, if it exists.
-$$\lim _ { h \rightarrow 8 } \frac { 2 } { \sqrt { 3 h + 4 } + 2 }$$
A) Does not exist
B) 1/2
C) 1
D) 2

Question

Quizplus · Accepted Answer

We can find the limit by plugging in 8 for h:
$$\frac { 2 } { \sqrt { 3 \cdot 8 + 4 } + 2 } = \frac{2}{\sqrt{28}+2} = \frac{2}{2\sqrt{7}+2} = \frac{1}{\sqrt{7}+1}\cdot\frac{\sqrt{7}-1}{\sqrt{7}-1} = \frac{\sqrt{7}-1}{6}$$
Therefore, the limit exists and is equal to $\frac{\sqrt{7}-1}{6}$. The closest choice is B, which is $\frac{1}{2}$. However, this is not the exact value of the limit, so B is the best choice.

Find the Limit, If It Exists lim⁡h→823h+4+2\lim _ { h \rightarrow 8 } \frac { 2 } { \sqrt { 3 h + 4 } + 2 }h→8lim​3h+4​+22​

Find the Limit, If It Exists $\lim _ { h \rightarrow 8 } \frac { 2 } { \sqrt { 3 h + 4 } + 2 }$