Graphically Approximate the Limit (If It Exists)by Using a Graphing $\lim _ { x \rightarrow 0 ^ { - } } \frac { \sqrt { x + 5 } - \sqrt { 5 } } { x }$

question 54

Multiple Choice

Graphically approximate the limit (if it exists) by using a graphing utility to graph the function.Round your answer to four decimal places. $\lim _ { x \rightarrow 0 ^ { - } } \frac { \sqrt { x + 5 } - \sqrt { 5 } } { x }$

• A) \(\lim _ { x \rightarrow 0 ^ { - } } \frac { \sqrt { x + 5 } - \sqrt { 5 } } { x } \approx - 0.7236\)
• B) \(\lim _ { x \rightarrow 0 ^ { - } } \frac { \sqrt { x + 5 } - \sqrt { 5 } } { x } \approx 1.2236\)
• C) \(\lim _ { x \rightarrow 0 ^ { - } } \frac { \sqrt { x + 5 } - \sqrt { 5 } } { x } \approx 0.2236\)
• D) \(\lim _ { x \rightarrow 0 ^ { - } } \frac { \sqrt { x + 5 } - \sqrt { 5 } } { x } \approx 0.7236\)
• E) \(\lim _ { x \rightarrow 0 ^ { - } } \frac { \sqrt { x + 5 } - \sqrt { 5 } } { x } \approx - 0.2764\)

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Definitions:

Basilar Membrane

A structural element within the cochlea of the inner ear, critical in the process of sound perception and auditory signal transduction.

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Difference Threshold

The minimum amount of change needed in a stimulus for the difference to be noticeable.