Continuous Real Function on Closed Interval/Examples/Reciprocal of 1 + e to the Reciprocal of x

Examples of Continuous Real Functions on Closed Intervals

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 $\closedint 0 1$.

Sources

• 1961: David V. Widder: Advanced Calculus (2nd ed.) ... (previous) ... (next): $1$ Partial Differentiation: $\S 2$. Functions of One Variable: $2.1$ Limits and Continuity