What is the value of $\frac{\sin x}x$ at $x=0$? On plotting graph for $\frac{\sin x}{x}$ using Wolfram|Alpha and Google, got that :

also, I can get the value of $\lim_{x\rightarrow 0} \frac{\sin x}{x} = 1$ using squeeze theorem and as illustrated on sources such as MIT. 
But I'm not able to understand how the function is defined at $x=0$ and its value came out to be $1$ at that point. As promised in the plot for the function.
Using limits I got the idea about the behavior of the function in the neighborhood of that point but not its value exactly at $x=0$.

The function is not defined at $x=0$.
But it can be continuously extended (since the limit from the left is equal to the limit from the right).
So the graph is not technically correct, it just shows the extended function.
