How do you find the vertical, horizontal or slant asymptotes for $y = \frac{x}{e^{x}}$ $y= x / e^x$ ?

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Answer 1 · 2016-11-16T15:24:57

The horizontal asymptote is $y = 0$ $y=0$
No slant or vertical asymptote.

The exponential function $e^{x}$ $e^x$ is always positive.

$AA x inRR, e^x>0$

So we don't have a vertical asymptote:

$lim_(x->-oo)y=x/e^(-oo)=(-oo*e^(oo))=-oo$

$lim_(x->+oo)y=x/e^(+oo)=(x/e^(oo))=0^(+)$

We have a horizontal asymptote $y=0$

graph{(y-x/e^x)(y)=0 [-6.29, 7.757, -4.887, 2.136]}

How do you find the vertical, horizontal or slant asymptotes for y= x / e^xy=xexy= x / e^x?