How do you find the limit $lima^x$ as $x->oo$ ?

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Answer 1 · 2016-12-31T19:23:34

Use $a^x = e^(xlna)$ and consider cases.

For $0 < a < 1$ , we have $lna < 0$ , so

as $xrarroo$ , we get $xlnararr-oo$ and so $a^x rarr 0$ .

For $a=0$ , we get the indeterminate form $1^oo$ .

For $a > 1$ , we have $lna > 0$ , so

as $xrarroo$ , we get $xlnararroo$ and so $a^x rarr oo$ .

How do you find the limit lima^xlima^x as x->oox->oo?