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given f(x)=e^-x^3 find the vertical and horizontal asymptotes

Sagot :

Given:

[tex]f\mleft(x\mright)=e^{-x^3}[/tex]

To find the vertical and horizontal asymptotes:

The line x=L is a vertical asymptote of the function f(x) if the limit of the function at this point is infinite.

But, here there is no such point.

Thus, the function f(x) doesn't have a vertical asymptote.

The line y=L is a vertical asymptote of the function f(x) if the limit of the function (either left or right side) at this point is finite.

[tex]\begin{gathered} y=\lim _{x\rightarrow\infty}e^{-x^3} \\ =e^{-\infty} \\ y=0 \\ y=\lim _{x\rightarrow-\infty}e^{-x^3} \\ y=e^{\infty} \\ =\infty \end{gathered}[/tex]

Thus, y = 0 is the horizontal asymptote for the given function.

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