Answer
$\underset{x\to 3}{\mathop{\lim }}\,\left( 2x-1 \right)=5$, because as x-approaches 3, the value of $ f\left( x \right)$ gets closer to 5.
Work Step by Step
Consider the provided function, $ f\left( x \right)=\left( 2x-1 \right)$.
This function $ f\left( x \right)=\left( 2x-1 \right)$ is in the form of $ y=mx+b $, where ‘ $ m $ ’ is the slope and ‘ $ b $ ’ is the y-intercept.
Compare the function $ f\left( x \right)=\left( 2x-1 \right)$ with $ y=mx+b $
Hence, here the slope $\left( m \right)$ is 2 and the y-intercept $\left( b \right)$ is $-1$.
To graph the function $ f\left( x \right)=\left( 2x-1 \right)$ using slope and y-intercept, follow the following steps.
Step 1: Consider the $ xy $ axis with origin at $\left( 0,0 \right)$.
Step 2: Plot the y-intercept $\left( 0,b \right)$ which is the point $\left( 0,-1 \right)$ in the $ xy $ axis. This point is always lying on the vertical axis y.
Step 3: From the y-intercept, plot another point using the slope. Here the slope is $ m=\frac{y}{x}=2$; that means from the y-intercept move 2 units up and 1 unit right.
Now, consider the provided limit, $\underset{x\to 3}{\mathop{\lim }}\,f\left( x \right)$, where $ f\left( x \right)=\left( 2x-1 \right)$.
Consider the obtained graph of the function $ f\left( x \right)=\left( 2x-1 \right)$.
To find $\underset{x\to 3}{\mathop{\lim }}\,\left( 2x-1 \right)$, examine the portion of the graph near $ x=3$.
As x gets closer to 3, the value of $ f\left( x \right)$ gets closer to the y-coordinate of 5. This point $\left( 3,5 \right)$ is as shown in the above graph.
The point $\left( 3,5 \right)$ has a y-coordinate of 5.
Thus, $\underset{x\to 3}{\mathop{\lim }}\,\left( 2x-1 \right)=5$.
Hence the value of $\underset{x\to 3}{\mathop{\lim }}\,\left( 2x-1 \right)$ is 5.
