Question

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

$\underset{x\to 0}{lim}f\left(x\right),f\left(x\right)=\left\{\begin{array}{c}x\\ 1\\ 3x\end{array}\right.\begin{array}{c}if,x<0\\ if,x=0\\ if,x>0\end{array}$

Short answer

The limit of the function (at x= 0) is = 0

Step-by-step solution

Step1. Given information 

The given function $\underset{x\to 0}{lim}f\left(x\right),f\left(x\right)=\left\{\begin{array}{c}x\\ 1\\ 3x\end{array}\right.\begin{array}{c}if,x<0\\ if,x=0\\ if,x>0\end{array}$

Step2. Calculations of the value of the function at limit points 

To find the limit we have to draw the graph of its

We know that at the limit point as x-factor is near to limit points so that time y tends to a specific value, that specific value is the value of the function at the limit point

so according to the question, we can see in the pieces of both graphs when x is near 0, then y approach 0,

but $atx=0,y=1$

Thus the limit of the given function is evaluated by 0