Use a CAS to Plot the Function near the Point $f ( x )$

question 149

Multiple Choice

Use a CAS to plot the function near the point x0 being approached. From your plot guess the value of the limit.
-What conditions, when present, are sufficient to conclude that a function $f ( x )$ has a limit as $x$ approaches some value of a?

• A) The limit of \(f ( x )\) as \(x \rightarrow a\) from the left exists, the limit of \(f ( x )\) as \(x \rightarrow\) from the right exists, and these two limits are the same.
• B) The limit of \(f ( x )\) as \(x \rightarrow\) a from the left exists, the limit of \(f ( x )\) as \(x \rightarrow\) from the right exists, and at least one of these limits is the same as \(f ( a )\).
• C) Either the limit of \(f ( x )\) as \(x \rightarrow a\) from the left exists or the limit of \(f ( x )\) as \(x \rightarrow a\) from the right exists
• D) \(f ( a )\) exists, the limit of \(f ( x )\) as \(x \rightarrow\) from the left exists, and the limit of \(f ( x )\) as \(x \rightarrow\) from the right exists.

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Definitions:

Multiaxial Joints

Joints that allow movement around several axes, thus enabling motion in multiple planes such as the shoulder and hip joints.

Extension

Extension is a movement that increases the angle between two body parts, such as straightening a flexed knee.

Bending Forward

A physical movement where the upper body moves closer to the legs, often used in exercises or as a stretch.

Shrugging Shoulders

A movement involving elevation of the shoulders, often as a gesture of indifference or to activate specific muscles in the upper body.