How do you show $\lim\limits_{h \to 0} \frac{a^h-1}{h} = 1$ when a = e?

Asked Apr 21 '20 at 23:11

Active Apr 21 '20 at 23:15

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This limit appears using the definition of a derivative applied to an exponential function. I understand the implications but I don't know how to show the basic result.

edited Apr 21 '20 at 23:15

asked Apr 21 '20 at 23:11

Ben Mills

It depends on your definition of $e.$ Some people take the definition of $e$ to be the value of $a$ for which that limit equals $1$. – B. Goddard Apr 21 '20 at 23:15
Cf. this question – J. W. Tanner Apr 21 '20 at 23:27

How do you show $\lim\limits_{h \to 0} \frac{a^h-1}{h} = 1$ when a = e?

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