Explanation Given : f ( x ) = sin x , K = 1 2 Concept used: Intermediate value theorem: Intermediate value theorem states that if f is a continuous function whoch domain contains the interval [ a , b ] , then it takes on any given value between f ( a ) and f ( b ) at some point within the interval f ( c ) = K where c ∈ ( a , b ) . Continuity: The function f is continuous at x = c if f ( c ) is defined and if lim → x → c f ( x ) = f ( c ) . Calculation: f ( x ) = sin x , K = 1 2 be a given function. It has to find interval [ a , b ] , and value K there is some c ∈ ( a , b ) for which f ( c ) = K

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 1.4, Problem 63S

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To show:A fuction f has a value K , there must be some c∈ℝ for which f(c)=K by using the intermediate value theorem and find or approximateonesuch value of c .

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Chapter 1.4, Problem 62S

Chapter 1.4, Problem 64S

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Chapter 1 Solutions

Calculus

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ACP Ch. 1 - Prob. BCP Ch. 1 - Prob. CCP Ch. 1 - Prob. DCP

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A fuction f has a value K , there must be some c ∈ ℝ for which f ( c ) = K by using the intermediate value theorem and find or approximateonesuch value of c .

Solution Summary: The author states that if f is a continuous function, it takes on any given value at some point within the interval.

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To show:A fuction f has a value K , there must be some c∈ℝ for which f(c)=K by using the intermediate value theorem and find or approximateonesuch value of c .

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Chapter 1 Solutions