$x \mapsto e^x$ on $\reals$

Example · High school

Terms

Term	This example	Why
continuous	✓	$x \mapsto e^x$ is continuous.
analytic	✓	$e^x$ is analytic on $\reals$, because it equals the power series $1 + x + \frac{x^2}{2} + \frac{x^3}{6} + \dots$ for every $x$.
uniformly continuous	✗	$x \mapsto e^x$ is not uniformly continuous, because its graph gets steeper without bound as $x$ increases.

Distinctions using this example

• Continuous vs. uniformly continuous

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