# Calculus

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Consider the function f(x)=8.5x−cos(x)+2 on the interval 0¡Üx¡Ü1 . 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 ______¡Ük¡Ü______

there is a c in 0 ¡Üc¡Ü 1

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What is "c in 0 ¡Üc¡Ü 1" ?

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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.

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