Explanation Theorem Used: Root location theorem: If f is continuous on the closed interval [ a , b ] and if f ( a ) and f ( b ) have opposite algebraic signs (one positive and the other negative), then f ( c ) = 0 for at least one number c on the open interval ( a , b ) . The statement “the equation x + sin x = 1 x + 3 has at least one solution on the interval ( 0 , π ) ” is equivalent to the statement “the function f ( x ) = x + sin x − 1 x + 3 has at least one solution on the interval ( 0 , π ) ”. The function f ( x ) is continuous on the closed interval [ 0 , π ]

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 2, Problem 30PE

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To show: the equation x+sinx=1x+3 has at least one solution on the interval (0,π) .

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Chapter 2, Problem 29PE

Chapter 2, Problem 1SP

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Chapter 2 Solutions

Calculus

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the equation x + sin x = 1 x + 3 has at least one solution on the interval ( 0 , π ) .

Solution Summary: The author explains that the function f(x) has at least one solution on the interval

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To show: the equation x+sinx=1x+3 has at least one solution on the interval (0,π) .

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Chapter 2 Solutions