Find the limit.
-$\lim _ { x \rightarrow 2 ^ { + } } \sqrt { \frac { 7 x ^ { 2 } } { 10 + x } }$
A) $\sqrt { - \frac { 7 } { 4 } }$
B) $\frac { 7 } { 2 }$
C) $\sqrt { \frac { 7 } { 2 } }$
D) Does not exist

Question

Quizplus · Accepted Answer

As x approaches 2 from the positive side, the denominator of the fraction approaches 12 and the numerator approaches 28. Thus, we have:

\begin{align*} \lim _ { x ightarrow 2 ^ { + } } \sqrt { \frac { 7 x ^ { 2 } } { 10 + x } } &= \lim _ { x ightarrow 2 ^ { + } } \sqrt{\frac{7x^2}{12}} \
&= \sqrt{\frac{7}{12}} \lim _ { x ightarrow 2 ^ { + } } x \
&= \sqrt{\frac{7}{2}} \end{align*}

Therefore, the answer is choice C.

Find the Limit lim⁡x→2+7x210+x\lim _ { x \rightarrow 2 ^ { + } } \sqrt { \frac { 7 x ^ { 2 } } { 10 + x } }limx→2+​10+x7x2​​

Find the Limit $\lim _ { x \rightarrow 2 ^ { + } } \sqrt { \frac { 7 x ^ { 2 } } { 10 + x } }$