(a) Explanation Given: f 1 ( x ) and f 2 ( x ) be continuous functions on closed interval [ a , b ] and f 1 ( a ) < f 2 ( a ) ⇒ f 1 ( a ) − f 2 ( a ) < 0 and f 1 ( b ) > f 2 ( b ) ⇒ f 1 ( b ) − f 2 ( b ) > 0 Formula Used: Proof: A function f ( x ) = f 1 ( x ) − f 2 ( x ) is also a continuous function, because difference of two continuous function is again a continuous function b) To determine To Prove: There exists c in [ 0 , π 2 ] such that cos x = x and approximate the value of c to three decimal points by using graphing utility.

11th Edition

ISBN: 9781337275361

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 1.4, Problem 128E

(a)

To determine

To Prove: f1(c) =f2(c) if f1(x) and f2(x) be continuous functions on closed interval [a, b] and f1(a)<f2(a), f1(b)>f2(b)

To determine

To Prove: There exists c in [0, π2] such that cosx=x and approximate the value of c to three decimal points by using graphing utility.

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Chapter 1.4, Problem 127E

Chapter 1.4, Problem 129E

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Chapter 1 Solutions

Calculus of a Single Variable

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To Prove: f 1 ( c ) = f 2 ( c ) if f 1 ( x ) and f 2 ( x ) be continuous functions on closed interval [ a , b ] and f 1 ( a ) < f 2 ( a ) , f 1 ( b ) > f 2 ( b )

Solution Summary: The author explains that if f_1(x) is a continuous function on closed interval, the difference between the two continuous functions is also continuous. Substituting

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To Prove: f1(c) =f2(c) if f1(x) and f2(x) be continuous functions on closed interval [a, b] and f1(a)<f2(a), f1(b)>f2(b)

To Prove: There exists c in [0, π2] such that cosx=x and approximate the value of c to three decimal points by using graphing utility.

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Chapter 1 Solutions

To Prove: f 1 ( c ) = f 2 ( c ) if f 1 ( x ) and f 2 ( x ) be continuous functions on closed interval [ a , b ] and f 1 ( a ) &lt; f 2 ( a ) , f 1 ( b ) &gt; f 2 ( b )

Solution Summary: The author explains that if f_1(x) is a continuous function on closed interval, the difference between the two continuous functions is also continuous. Substituting

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To Prove: f1(c) =f2(c) if f1(x) and f2(x) be continuous functions on closed interval [a, b] and f1(a)<f2(a), f1(b)>f2(b)

To Prove: There exists c in [0, π2] such that cosx=x and approximate the value of c to three decimal points by using graphing utility.

Want to see the full answer?

Chapter 1 Solutions

To Prove: f 1 ( c ) = f 2 ( c ) if f 1 ( x ) and f 2 ( x ) be continuous functions on closed interval [ a , b ] and f 1 ( a ) < f 2 ( a ) , f 1 ( b ) > f 2 ( b )