Questions: Which of the following is/are signified by the limit as x approaches a of f(x) equals infinity? - This means that f(a) equals infinity - The value of x goes out to infinity, when it gets close to a. - As x approaches a, the value of f(x) increases without bound. - The limit exists and equals infinity. - The value of fk(x) becomes infinite when x approaches a.

Solution Steps

The problem involves evaluating the limit of a function \( f(x) \) as \( x \) approaches a certain value. Specifically, it asks to determine the implications of the given limits.

The given information states:

1. \( \lim_{x \to a} f(x) = 3 \)
2. \( \lim_{x \to a^+} f(x) = 3 \)
3. \( \lim_{x \to a^-} f(x) = 3 \)

From the given information, we can conclude that:

• The limit of \( f(x) \) as \( x \) approaches \( a \) from the left (\( x \to a^- \)) is 3.
• The limit of \( f(x) \) as \( x \) approaches \( a \) from the right (\( x \to a^+ \)) is 3.
• Therefore, the overall limit of \( f(x) \) as \( x \) approaches \( a \) is 3.

Final Answer