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Math Help - find limits for the functions

  1. #1
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    find limits for the functions

    f(x)= x^2/x^2+x-2

    lim
    x--> - infinity f(x)

    lim
    x--> infinity f (x)

    I know the answers for both are 1, however does anyone know if it is 1- or 1+?

    Also, how can you tell by looking at the graph on the calculator?
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  2. #2
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    Quote Originally Posted by phalange View Post
    f(x)= x^2/x^2+x-2

    lim
    x--> - infinity f(x)

    lim
    x--> infinity f (x)

    I know the answers for both are 1, however does anyone know if it is 1- or 1+?

    Also, how can you tell by looking at the graph on the calculator?
    Graph the equation on the calculator, and look for the behavior of the graph. If the graph is 1/x, for instance, it will go to 0 if x goes to positive infinity (look at the x-axis and pretend that you're going to the right of the x-axis).

    When you say 1+ or 1- are you referring to positive 1 and negative 1 or "as x goes to 1 from the left or right side?"
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  3. #3
    MHF Contributor Calculus26's Avatar
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    Florida
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    If by 1+ and 1- you're asking does f approach 1 from above or below ?

    1)you could solve f(x) = 1

    2)note f = x^2/(x+2)(x-1) > 0 if x >1 or x < -2

    if you do you get x =2 which means f crosses the horizontal asymptote at x= 2

    combining 1) and 2) like Sherlock Holmes

    f -> 1 from below as x - > infinity and from above as x-> -infinity
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