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Finding the horizontal asymptote

  1. Nov 26, 2008 #1
    How do i find the horizontal asymptote for f(x)=xe-x2

    thanks for the help.
  2. jcsd
  3. Nov 26, 2008 #2


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    Staff Emeritus
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    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.
  4. Nov 26, 2008 #3
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