# Category:Examples of Continuous Real Functions

Jump to navigation
Jump to search

This category contains examples of Continuous Real Function.

### Continuity at a Point

**$f$ is continuous at $x$** if and only if the limit $\ds \lim_{y \mathop \to x} \map f y$ exists and:

- $\ds \lim_{y \mathop \to x} \map f y = \map f x$

### Continuous Everywhere

Let $f: \R \to \R$ be a real function.

Then $f$ is **everywhere continuous** if and only if $f$ is continuous at every point in $\R$.

### Continuity on a Subset of Domain

Let $A \subseteq \R$ be any subset of the real numbers.

Let $f: A \to \R$ be a real function.

Then **$f$ is continuous on $A$** if and only if $f$ is continuous at every point of $A$.

## Pages in category "Examples of Continuous Real Functions"

The following 8 pages are in this category, out of 8 total.

### C

- Continuous Real Function on Closed Interval/Examples
- Continuous Real Function on Closed Interval/Examples/Reciprocal of 1 + e to the Reciprocal of x
- Continuous Real Function/Examples
- Continuous Real Function/Examples/Root of x at 1
- Continuous Real Function/Examples/Sine of Reciprocal of x
- Continuous Real Function/Examples/Sine of x over x with 1 at 0