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Math Help - Prove this limit

  1. #1
    Member sluggerbroth's Avatar
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    Prove this limit

    lim as x goes to 1 (x^(2)-2x+4)=3
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  2. #2
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    Re: Prove this limit

    If a function f is continuous at x0, then its limit as x -> x0 is f(x0).
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  3. #3
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    Re: Prove this limit

    Using what "basis"? If you know about "continuous functions" and in particular that all polynomials are continous for all values of x then it is sufficient to say, as emakarov does, that the limit is (1)^2-2(1)+ 4= 1- 2+ 4= 3.

    If, on the other hand, you have only the definition of limit to work with, you need to look at |f(x)- L|= |x^2- 2x+ 4- 3|= |x^2- 2x+ 1|= |x-1|^2< \epsilon, then what can you say if you choose \delta= \sqrt{\epsilon} so that |x- 1|< \delta becomes |x- 1|< \sqrt{\epsilon}?
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  4. #4
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    Re: Prove this limit

    The function f(x) = x^2 - 2x + 4 is continuous everywhere.

    Therefore \lim_{x \to 1} (x^2 - 2x + 4) = (1)^2 - 2(1) + 4 = 3
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