Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +$\infty$or -$\infty$. $$\lim _ { x \rightarrow 4 ^ { - } } \frac { \sqrt { x } - 2 } { x - 4 }$$
A) $- \frac { 1 } { 4 }$
B) $\frac { 1 } { 4 }$
C) 2
D) -2

Question

Quizplus · Accepted Answer

The limit can be evaluated by applying L'Hôpital's Rule, which is used when the limit initially gives an indeterminate form like 0/0. Differentiating the numerator and the denominator separately gives: $$\lim _ { x \rightarrow 4 ^ { - } } \frac { \frac { 1 } { 2 \sqrt { x } } } { 1 } = \frac { 1 } { 2 \sqrt { 4 } } = \frac { 1 } { 4 }$$.

Find the Indicated One-Sided Limit ∞\infty∞ Or - ∞\infty∞ lim⁡x→4−x−2x−4\lim _ { x \rightarrow 4 ^ { - } } \frac { \sqrt { x } - 2 } { x - 4 }x→4−lim​x−4x​−2​

Find the Indicated One-Sided Limit $\infty$ Or - $\infty$ $\lim _ { x \rightarrow 4 ^ { - } } \frac { \sqrt { x } - 2 } { x - 4 }$