How do you find the horizontal asymptote of x3 times ex?

Answer 1

y=x3ex

your first bet is to find the domain, the set of all possible x values

for x3 and e2

in this case theres no restriictions in the domain meaning any real number can be used so you can consider everything properly

noww look at each segment x3 and ex as x approaches negative and positive infinity

as as x approaches positive infinity x3 and ex both approach positive infinity

no asymptote is seen

BUT as x approaches negative infinity x3approaches negative infinity while ex approaches 0. now you have to see which one of the two moves faster

ex approaches zero much faster than x3 approaches negative infinity

so the horizontal asymptote is 0