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Calculus

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Consider the function f(x) = 8.5 x − cos(x) + 2 on the interval 0 ¡Ü x ¡Ü 1. The Intermediate Value Theorem guarantees that there is a value c such that f(c) = k for which values of c and k? Fill in the following mathematical statements, giving an interval with non-zero length in each case.

For every k in ____ ¡Ü k ¡Ü___ ,
there is a c in 0 ¡Ü c ¡Ü 1
such that f(c) = k.

  • Calculus -

    Sorry...
    Again...
    Before I posted the question, I could see the symbols...
    Consider the function f(x) = 8.5 x − cos(x) + 2 on the interval 0 less than or equal to x less than or equal to 1. The Intermediate Value Theorem guarantees that there is a value c such that f(c) = k for which values of c and k? Fill in the following mathematical statements, giving an interval with non-zero length in each case.

    For every k in ______ less than or equal to k less than or equal to ______ ,
    there is a c in 0 less than or equal to c less than or equal to 1
    such that f(c) = k.

  • Calculus -

    "Consider the function f(x) = 8.5 x − cos(x) + 2 on the interval 0 less than or equal to x less than or equal to 1.

    The Intermediate Value Theorem guarantees that there is a value c such that f(c) = k for 0≤c≤1 and f(0)≤k≤f(1), if f(1)≥f(0), and f(0)≥k≥f(1) if f(1)<f(0)."

    In this case, f(0)<f(1), so the first case applies.

    P.S.
    If you have difficulties getting the symbols, you have one of the two options:
    1. For Firefox, goto view/character encoding and choose Western 8859-1.
    For IE, choose a similar option.
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    2. Type the following without the spaces between characters:
    ≤ & l e ;
    ≥ & g e ;

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