2nd Edition

ISBN: 9781133490975

Author: Stewart, James

Publisher: Cengage Learning

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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 4.2, Problem 26E

Suppose that f and g are continuous on [a, b] and differentiable on (a, b). Suppose also that f(a) = g(a) and f′(x) < g′(x) for a < x < b. Prove that f(b) < g(b). [Hint: Apply the Mean Value Theorem to the function h = f − g.]

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Chapter 4.2, Problem 25E

Chapter 4.2, Problem 27E

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Chapter 4 Solutions

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Suppose that f and g are continuous on [ a , b ] and differentiable on ( a , b ). Suppose also that f ( a ) = g ( a ) and f ′( x ) < g ′( x ) for a < x < b . Prove that f ( b ) < g ( b ). [ Hint: Apply the Mean Value Theorem to the function h = f − g. ]

Solution Summary: The author explains how the function f(b)g () is a function that satisfies the following conditions.

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Chapter 4 Solutions

Suppose that f and g are continuous on [ a , b ] and differentiable on ( a , b ). Suppose also that f ( a ) = g ( a ) and f ′( x ) &lt; g ′( x ) for a &lt; x &lt; b . Prove that f ( b ) &lt; g ( b ). [ Hint: Apply the Mean Value Theorem to the function h = f − g. ]

Solution Summary: The author explains how the function f(b)g () is a function that satisfies the following conditions.

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Chapter 4 Solutions

Suppose that f and g are continuous on [ a , b ] and differentiable on ( a , b ). Suppose also that f ( a ) = g ( a ) and f ′( x ) < g ′( x ) for a < x < b . Prove that f ( b ) < g ( b ). [ Hint: Apply the Mean Value Theorem to the function h = f − g. ]