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:

Uterine Wall

The internal lining of the uterus, which thickens during the menstrual cycle in preparation for possible implantation of an embryo.

Birth Canal

The passage consisting of the cervix, vagina, and vulva through which a fetus travels during childbirth.

Rh Disease

A medical condition where an incompatibility between the blood types of a pregnant mother and her unborn child causes hemolytic disease in the fetus.

Red Blood Cells

Cells in the blood responsible for carrying oxygen from the lungs to the rest of the body, also known as erythrocytes.