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Homework Help: Questions about limits.

  1. Mar 25, 2007 #1
    I have 2 questions about limits :

    1)Evaluate : lim as x approaches infinity for
    (3x-4-4x^2) / (x^2 -16)

    2)Evaluate: lim as x approaches -27 for
    (27+x) / ( 7/2 + 3 )

    thank u.
  2. jcsd
  3. Mar 25, 2007 #2


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    If you show us some work, we will be glad to help you.
  4. Mar 25, 2007 #3
    Sorry about that.....heres my work
    http://img88.imageshack.us/img88/9971/img002sy9.png [Broken]
    Last edited by a moderator: May 2, 2017
  5. Mar 25, 2007 #4
    for #1, in order to find the limit as x approaches infinity you need to divide the numerator/denominator by the highest power of x in the denominator, in this problem it would be x^2.
    Doing this you'd end up with some 1/x's or x^n times some constant (1,2,3,...) which =0 when you take their limit as x approaches infinity

    for #2, lim as x approaches a for f(x) = f(a) IF a is in the domain of f
    Last edited: Mar 25, 2007
  6. Mar 25, 2007 #5
    For #2, when you plug -27 in you get a number over a nonzero. That means the limit equals the value of the function, in this case, 0
  7. Mar 25, 2007 #6
    what about Q.1 i still dont understand how to solve it using infinity???
  8. Mar 25, 2007 #7
    In the limit, only the highest degree matters. Because the numerator and denominator have the same degree, the function will have a limit (horizontal asymtote) approaching infinity. Divide the coefficient of the numerator by the coefficient of the denominator and you have all thats left when x is big. Your post is different from your work, but either way the answer should be apparent in 2 seconds
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