Continuous Real Function/Examples/Sine of x over x with 1 at 0

Examples of Continuous Real Functions
Let $f: \R_{\ge 0} \to \R$ be the real function defined as:
 * $\map f x = \begin {cases} \dfrac {\sin x} x & : x \ne 0 \\ 1 & : x = 0 \end {cases}$

Then $\map f x$ is continuous at $x = 0$.

Proof
From Limit of $ \dfrac {\sin x} x$, we have that:

The result follows by definition of continuous real function.