How do you find the horizontal asymptote for $g(x)=e^x-2$ ?

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Answer 1 · 2016-01-14T01:24:06

Evaluate x at both $+-oo$

$""_(xrarroo)^"lim"(e^x-2)=oo$

So, the right limit, as $xrarroo$ , has no horizontal asymptote.

However, the left limit does have an asymptote:

$""_(xrarr-oo)^"lim"(e^x-2)=0-2=-2$

So, the left limit, as $xrarr-oo$ , has horizontal asymptote $=-2$ .

hope that helped

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How do you find the horizontal asymptote for g(x)=e^x-2g(x)=e^x-2?