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Math Help - Infinity proving

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    Infinity proving

    Suppose f : D --> R is a function whose domain contains (-infinity, a) for some a \inR. We define lim x--> - infinity f(x) = infinityto mean for all M >0 there exists K <0 such that

    x < K ==> f(x) > M.

    We define lim x--> - infinity f(x) = - infinity to mean for all M < 0 there exists K < 0 such that

    x < K ==> f(x) < M.


    Suppose n is a positive integer and let P:R --> R be a polynomial function defined by
    P(x) = anx^n + an-1x^(n-1) + ... + a0 for all x \in R.

    (a) Suppose that n is odd and an is positive. Prove that lim x--> - infinity P(x) = - inifinity. (Hint: You may use that x^n < xfor all x < -1)

    (b) Prove that if n is even and an is positive then lim x--> - infinity P(x) = inifinity. (Hint: replacing P with -P) Do not do this
    lim x--> - infinity  -P(x) = - lim x--> -infinity P(x) =  - (- infinity) = infinity.

    (c) Prove that if n is even and an is positive then lim x--> - infinity P(x) = infinity.
    Last edited by 450081592; November 25th 2009 at 07:25 PM.
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