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Math Help - limits of infinity

  1. #1
    Super Member
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    limits of infinity

    Which of the following limits equal infinity ( but not + infinity or - infinity)

    a) lim (x->0) sinx/x^2

    b) lim (x->3) (x+3) / (x^2 - 9)

    Im not sure how to determine if it's +inf., -inf., or just infinity

    Please help....Thanks.
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  2. #2
    Senior Member
    Joined
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    Hello jzellt!

    Quote Originally Posted by jzellt View Post
    Which of the following limits equal infinity ( but not + infinity or - infinity)

    a) lim (x->0) sinx/x^2

    b) lim (x->3) (x+3) / (x^2 - 9)

    Im not sure how to determine if it's +inf., -inf., or just infinity

    Please help....Thanks.
    Did you ever hear about the Rule of L'Hospital?

    a) lim (x->0) sinx/x^2

    lim (x->0) sinx = 0 and lim (x->0) x^2 = 0

    So [sin(x)]' = cos(x) and [x^2]' = 2x

    Thus lim (x->0) sinx/x^2 = lim (x->0) cosx/(2x)

    It is lim (x->0) cosx = 1 and lim(x->0)2x = 0

    So

    lim (x->0) cosx/(2x) = \pm \infty

    b) lim (x->3) (x+3) / (x^2 - 9)

    You want to find the limes of +3? You are sure about that? In that case it is
    lim (x->3) (x+3) / (x^2 - 9) = \pm \infty

    because (x+3) -> 6, if x->3

    and x^2-9 -> 0, if x -> 0

    Regards
    Rapha
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