Q. 72 - Calculus

Question

Use calculator graphs to make approximations for each of the limits in Exercises 67–74.  

$\underset{x\to \infty }{\lim }\frac{\ln x}{x}$

Step-by-Step Solution

Answer

The approximated value of the limit is $\underset{x\to \infty }{\lim }\frac{\ln x}{x}=0$ by using the calculator graph.

The graph is

Step 1. Given Information.

The given limit is $\underset{x\to \infty }{\lim }\frac{\ln x}{x}.$

Step 2. Approximating the limit by using the calculator graphs.

To approximate the limit by using the calculator graphs. Insert the function in the calculator then adjust the Window.

So, the graph is

From the graph, we can depict that for $x\to \infty$ the value of the function tends to $0.$

Thus, the limit expression has the value of $\underset{x\to \infty }{\lim }\frac{\ln x}{x}=0.$