Use a CAS to plot the function near the point x0 being approached. From your plot guess the value of the limit.
-$$\lim _ { x \rightarrow 0 } \frac { \sqrt { 64 - x } - 8 } { x }$$
A) $- \frac { 1 } { 16 }$
B) 16
C) $\frac { 1 } { 16 }$
D) 8

Question

Quizplus · Accepted Answer

The function simplifies to a form where, as $x$ approaches 0, the numerator approaches 0 and the denominator is 0, indicating a potential 0/0 indeterminate form. Using L'Hôpital's Rule or algebraic manipulation (rationalizing the numerator), we find the limit is $-\frac{1}{16}$.

Use a CAS to Plot the Function near the Point lim⁡x→064−x−8x\lim _ { x \rightarrow 0 } \frac { \sqrt { 64 - x } - 8 } { x }x→0lim​x64−x​−8​

Use a CAS to Plot the Function near the Point $\lim _ { x \rightarrow 0 } \frac { \sqrt { 64 - x } - 8 } { x }$