Question

$$\lim_{x \to 0^{+}} \frac{1}{3x}$$

Explanation:

Step1: Analyze the behavior of \(x\)

As \(x\to0^{+}\), \(x\) approaches \(0\) from the positive side, so \(x>0\) and \(x\) is very small.

Step2: Analyze the behavior of \(\frac{1}{3x}\)

Since \(x>0\) and \(x\to0\), then \(3x>0\) and \(3x\to0\). As the denominator \(3x\) approaches \(0\) from the positive side, \(\frac{1}{3x}\) will increase without bound.

Answer:

\(\lim_{x\to0^{+}}\frac{1}{3x}=+\infty\)