13. find the limit.\n\\(\\lim_{x\\to0^{+}}\\frac{1}{3x}\\)

Explanation:

Step1: Analyze the given limit

We have $\lim_{x\rightarrow0^{+}}\frac{1}{3x}$. As $x$ approaches $0$ from the positive - side ($x>0$ and $x$ gets infinitesimally small), the denominator $3x$ approaches $0$ while remaining positive.

Step2: Determine the value of the limit

When the numerator is a non - zero constant ($1$ in this case) and the denominator approaches $0$ from the positive side, the value of the fraction $\frac{1}{3x}$ approaches positive infinity. Mathematically, $\lim_{x\rightarrow0^{+}}\frac{1}{3x}=+\infty$.

Answer:

$+\infty$