Question

Graph each function. Use the graph to find the indicated limit, if it exists.

$\underset{x\to 1}{\lim }f\left(x\right),f\left(x\right)=\ln \left(x\right)$

Short answer

The limit is$0$.

Step-by-step solution

Step 1. Given Information  

We are given a function$f\left(x\right)=\ln \left(x\right)$ and we need to graph the function and find$\underset{x\to 1}{\lim }f\left(x\right)$.

Step 2. Plotting the graph 

So, the graph of the function $f\left(x\right)=\ln \left(x\right)$is

Step 3. Finding the limit   

To find the value of $\underset{x\to 0}{\lim }f\left(x\right)$we need to find the value of the function at $x=0$.

$$\begin{gathered} f\left(x\right)=\ln \left(x\right) \\ \Rightarrow f\left(1\right)=\ln \left(1\right) \\ \Rightarrow f\left(1\right)=0 \\ \therefore \underset{x\to 1}{\lim }f\left(x\right)=0 \end{gathered}$$