Use a CAS to Plot the Function near the Point $\lim _ { x \rightarrow 0 } \frac { 4 - \sqrt { 16 - x ^ { 2 } } } { x }$

question 118

Multiple Choice

Use a CAS to plot the function near the point x0 being approached. From your plot guess the value of the limit.
- $\lim _ { x \rightarrow 0 } \frac { 4 - \sqrt { 16 - x ^ { 2 } } } { x }$

• A) 8
• B) \(\frac { 1 } { 8 }\)
• C) \(\frac { 1 } { 4 }\)
• D) 0

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Definitions:

Ciliary Muscles

Muscle fibers in the eye that control the shape of the lens, enabling focusing on objects at different distances.

Suspensory Ligament

Fibrous tissues that connect organs or parts of organs to each other or to skeletal structures, often supporting or holding them in place.

Lens

A transparent structure inside the eye that focuses light rays onto the retina to create clear images.

Aqueous Humor

A clear fluid filling the space in the front of the eyeball between the lens and the cornea, involved in nutrient supply and intraocular pressure maintenance.