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Math Help - Limit of polynimials

  1. #1
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    Limit of polynimials

    If f and g and polynomials and lim(x approaches infinity) of [f(x)/g(x)] = L, L not 0, show that f and g are of the same degree.

    I just can't get this one!
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    Re: Limit of polynimials

    If f(x) is of degree n and g(x) is of degree m, then f(x)/g(x) is a polynomial of degree n - m with some fractional remainder that is negligable since it will go to 0.

    If n > m, then n - m > 0. Any positive degree polynomial will go to positive or negative infinity when x goes to infinity.

    If n < m, then n - m < 0. Any negative degree polynomial will go to 0 when x goes to infinity.

    If n = m, then n - m = 0, which means the quotient will be a constant. The limit of a constant is a constant.

    So the only way to get a nonzero constant as the limit is to have f(x) and g(x) have the same degree.
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