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Math Help - Intermediate Value Theorem

  1. #1
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    Intermediate Value Theorem

    Dont really understand how to do this problem.

    Use the Intermediate Value Theorem to show that there is a root of the equation in the given interval.

    e^(-x^2)) = x (0,1)
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  2. #2
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    Let f(x)=e^{-x^2}-x, observe that f is a continuous function. Since f(0)=1 and f(1)<0,(because e>1\Rightarrow e^{-1}<1 \Rightarrow e^{-1}-1<0) thanks to IVT, f(x)=0 in (0,1)\Rightarrow e^{-x^2}=x there.
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  3. #3
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    Quote Originally Posted by TastyBeverage View Post
    Dont really understand how to do this problem.

    Use the Intermediate Value Theorem to show that there is a root of the equation in the given interval.

    e^(-x^2)) = x (0,1)
    Hint: Let f(x) = e^{-x^2} - x. Now f(0) > 0 and f(1) < 0.

    EDIT: Somebody been faster.
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