trigonometry - How is $frac{sin(x)}{x} = 1$ at $x = 0$

I have a function: $$\text{sinc}(x) = \frac{\sin(x)}{x}$$ and the example says that: $\text{sinc}(0) = 1$, How is it true?

I know that $\lim\limits_{x \to 0} \frac{\sin(x)}{x} = 1$, But the graph of the function $\text{sinc}(x)$ shows that it's continuous at $x = 0$ and that doesn't make sense.

Answer

In an elementary book, they should define $\mathrm{sinc}$ like this $$ \mathrm{sinc}\; x = \begin{cases} \frac{\sin x}{x}\qquad x \ne 0 \\ 1\qquad x=0 \end{cases} $$ and then immediately prove that it is continuous at $0$.

In a slightly more advanced book, they will just say $$ \mathrm{sinc}\;x = \frac{\sin x}{x} $$ and the reader will understand that removable singularities should be removed.