Provide an Appropriate Response $\rightarrow$ A from the Left Exists, the Limit of F(x) As to Conclude

question 61

Multiple Choice

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

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Definitions:

Internal Attribution

The process of explaining one's own or another's behavior as due to personal, internal characteristics rather than external factors.

Ballet Dancing

A form of performance dance that originated in the Renaissance courts of Europe and has evolved into a highly technical form of dance with its own vocabulary.

Recreational Drug

Substances used primarily for leisure or enjoyment, often with psychoactive effects, rather than for medical purposes.

External Attribution Style

The tendency to attribute one's own actions and outcomes to external factors or situations beyond personal control.