Q. 66 - Calculus

Question

Calculate each limit in Exercises 35–80. 

$\underset{x\to \infty }{lim}(\ln 3x-\ln 2x)$

Step-by-Step Solution

Answer

The limit is $0.405$

Step 1. Given information

The given expression is $\underset{x\to \infty }{lim}(\ln 3x-\ln 2x)$

Step 2. Calculation

The limit is calculated as below, 

$$\begin{gathered} \underset{x\to \infty }{lim}(\ln 3x-\ln 2x)=\underset{x\to \infty }{lim}\left(\ln \left(\frac{3x}{2x}\right)\right) \\ =\underset{x\to \infty }{lim}\left(\ln \left(\frac{3}{2}\right)\right) \\ =\ln \left(\frac{3}{2}\right) \\ \approx 0.405 \end{gathered}$$