Finding the horizontal asymptote

[alpha01]

How do i find the horizontal asymptote for f(x)=xe^-x2

thanks for the help.

 

[HallsofIvy]

The same way you find a horizontal asymptote, if it exists, for any function: look at what happens for very large (positive or negative) values of x. If x is a very large positive number the e^-x2 "dominates": xe^-x2 goes to 0 so 0 is a horizontal asymptote. You can get the idea, though it is not a proof, by looking at, say, x= 1000: (1000)e^-1000000= very close to 0. For x a very large negative number, both x and e^-x2- there is no horizontal asymptote in that direction.

 

[alpha01]

thanks