Determine whether or not the following limit exists. If, so compute the limit. $\lim _ { x \rightarrow 3 }$ $\frac { \sqrt { x } - 4 } { x ^ { 3 } + 27 }$
A) does not exist
B) 0
C) $\frac { \sqrt { 3 } - 4 } { 54 }$
D) $\sqrt { 3 }$ - 4
E) none of these

Question

Quizplus · Accepted Answer

The limit as $x$ approaches 3 of the given function can be directly computed by substituting $x = 3$ into the function, since both the numerator and denominator are continuous functions and the denominator does not equal zero when $x = 3$. Thus, the limit is $\frac{\sqrt{3} - 4}{3^3 + 27} = \frac{\sqrt{3} - 4}{54}$.

Determine Whether or Not the Following Limit Exists lim⁡x→3\lim _ { x \rightarrow 3 }limx→3​

Determine Whether or Not the Following Limit Exists $\lim _ { x \rightarrow 3 }$