Explanation Let f ( x ) = sin x − cos x − 3 x , and observe that each root this function corresponding to a solution of the equation sin x − cos x = 3 x , now f ( − π 2 ) = − 1 + 3 π 2 > 0 a n d f ( 0 ) = − 1 < 0 Because f is continuous on ( − π 2 , 0 ) and f ( − π 2 ) f

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 4, Problem 17CRE

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Use the intermediate value theorem to prove that x−cosx=3x has a solution and use Rolle ’s Theorem to show that this solution is unique

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Chapter 4, Problem 16CRE

Chapter 4, Problem 18CRE

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2 prove that Dxy #Dx Dy

EXAMPLE 3 Find S X √√2-2x2 dx. SOLUTION Let u = 2 - 2x². Then du = Χ dx = 2- 2x² = 信 du dx, so x dx = du and u-1/2 du (2√u) + C + C (in terms of x).

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Chapter 4 Solutions

CALCULUS (CLOTH)

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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Use the intermediate value theorem to prove that x − cos x = 3 x has a solution and use Rolle ’s Theorem to show that this solution is unique

Solution Summary: The author explains how the intermediate value theorem proves that x-mathrmcosx=3x has a solution and uses Rolle's Theory to show that

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Use the intermediate value theorem to prove that x−cosx=3x has a solution and use Rolle ’s Theorem to show that this solution is unique

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Chapter 4 Solutions