Question

what happens as x approaches zero from the positive direction?

f(x) goes to zero
f(x) gets larger
f(x) gets larger in the negative direction

Explanation:

Identify the target direction of approach

Using the One-Sided Limits knowledge point

$$ x \to 0^+ $$

Analyze the corresponding table values

Using the Numerical Limits knowledge point

$$
LATEXBLOCK0
$$

Determine the behavior of the function

Using the Numerical Limits knowledge point

$$ \lim_{x \to 0^+} f(x) $$

The values of \(x\) decrease towards \(0\) from the positive side: \(1 \to 0.1 \to 0.01 \to 0.001\). This corresponds to the sequence of function values \(h \to g \to f \to e\).

Answer:

• f(x) goes to zero
• f(x) gets larger (Correct answer)
• f(x) gets larger in the negative direction