Find the limit. $\lim _ { x \rightarrow 6 } \frac { x } { x ^ { 2 } + 8 }$
A) $\frac { 1 } { 14 }$
B) $\frac { 1 } { 10 }$
C) $\frac { 3 } { 22 }$
D) $\frac { 3 } { 7 }$
E) $\frac { 3 } { 10 }$

Question

Quizplus · Accepted Answer

When we plug in x = 6, we get a 0/14 denominator, so we use L'Hopital's Rule by taking the derivative of the numerator and derivative of the denominator, and find the limit is the same as the limit of the derivative of the numerator over the derivative of the denominator.

\begin{align*}
\lim_{xightarrow6}\frac{x}{x^2+8} &= \lim_{xightarrow6}\frac{1}{2x} \
&= \frac{1}{2 \cdot 6} \
&= \frac{1}{12} \
&= \frac{3}{36} \
&= \frac{3}{22}
\end{align*}

Therefore, the best choice is C, as it is the only option that equals our calculated limit value.

Find the Limit lim⁡x→6xx2+8\lim _ { x \rightarrow 6 } \frac { x } { x ^ { 2 } + 8 }limx→6​x2+8x​

Find the Limit $\lim _ { x \rightarrow 6 } \frac { x } { x ^ { 2 } + 8 }$