Question

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

$\underset{x\to 0}{lim}f\left(x\right),f\left(x\right)=\left\{\begin{array}{ll}\sin \left(x\right)& ifx\le 0\\ x^2& ifx>0\end{array}\right.$

Short answer

The value of given function (at x= 0 ) is : 0

Step-by-step solution

Step1. Given information 

The given function $\underset{x\to 0}{lim}f\left(x\right),f\left(x\right)=\left\{\begin{array}{ll}\sin \left(x\right)& ifx\le 0\\ x^2& ifx>0\end{array}\right.$

Step2. checking the existence of the  limit at a given point 

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

Thus the limit of the given function is evaluated by 0