Q. 64 - Calculus

Question

Calculate each limit in Exercises 35–80. 

$\underset{x\to 0^{+}}{lim}\ln \left(\frac{1}{x}\right)$

Step-by-Step Solution

Answer

The limit is $-\infty$

Step 1. Given information

The given expression is $\underset{x\to 0^{+}}{lim}\ln \left(\frac{1}{x}\right)$

Step 2. Calculation

The limit is calculated as below, 

$$\begin{gathered} \underset{x\to 0^{+}}{lim}\ln \left(\frac{1}{x}\right)=\underset{x\to 0^{+}}{lim}\left(\ln 1-\ln x\right) \\ =0-\ln 0 \\ =0-\infty \\ =-\infty \end{gathered}$$