Continuous Real Function on Closed Interval/Examples

Examples of Continuous Real Functions on Closed Intervals

Example: $\dfrac 1 {1 + e^{1 / x} }$ on $\closedint 0 1$

Consider the real function $f$ defined as:

$f := \begin {cases} \dfrac 1 {1 + e^{1 / x} } & : x \ne 0 \\ 0 & : x = 0 \end {cases}$

Then $f$ is continuous on the closed interval $\closedint 0 1$.