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Math Help - find the polynomial problem

  1. #1
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    find the polynomial problem

    find the polynomial ft f(x) with the smallest degree so that
    \lim_{x->1}\frac{f(x)}{x-1}\=1
    and
    \lim_{x->2}\frac{f(x)}{x-2}\=2
    and
    \lim_{x->3}\frac{f(x)}{x-3}\=3

    pls how should i assume the ft?
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  2. #2
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    A hint

    Consider what the existence of those limits (and their finite, non-zero values) means for the values of f(x) at x=1, x=2, and x=3. What monomials must then be factors of the polynomial f(x)?

    --Kevin C.
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  3. #3
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    Quote Originally Posted by TwistedOne151 View Post
    Consider what the existence of those limits (and their finite, non-zero values) means for the values of f(x) at x=1, x=2, and x=3. What monomials must then be factors of the polynomial f(x)?

    --Kevin C.
    i think f(x) has x-1 x-2 x-3
    so i assume f(x)=a(x-1)(x-2)(x-3) is it right?
    but
    i can not slove the problem~
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  4. #4
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    Chialin4,

    Close. f(x)=(x-1)(x-2)(x-3)*p(x), where p(x) is a polynomial with nonzero values at x=1, x=2, and x=3. Consider what the limits say about p(x), and find the lowest degree polynomial that satisfies these conditions.

    --Kevin C.
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