Is it correct to say that $\lim_{x\to -\infty} e^x = \lim_{x\to \infty} \frac{1}{e^x}$?

Question

I just see it logical...

Actually I think I can claim that

$$\lim_{x\to -\infty} a^x = \lim_{x\to \infty} \frac{1}{a^x}$$

$a$ being a parameter.

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Is it correct?

Answer 1

Substitute:

$$y:=-x\;,\;\;\text{so that}\;\;x\to-\infty\iff y\to\infty\;,\;\;\text{and from here}:$$

$$\lim_{x\to-\infty} e^x=\lim_{y\to\infty} e^{-y}=\lim_{y\to\infty}\frac1{e^y}=0$$