Explanation It is given that f is a continuous increasing function on [ 0 , ∞ ) such that f ( x ) > 0 . Let us assume that f ( x ) > a , where a is any positive number. From the assumption, ∫ 0 ∞ f ( x ) d x ≥ ∫ 0 ∞ a d x . Simplify the inequality ∫ 0 ∞ f ( x ) d x ≥ ∫ 0 ∞ a d x as follows. ∫ 0 ∞ f ( x ) d x ≥ ∫ 0 ∞ a d x ∫ 0 ∞ f ( x )

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ISBN: 9780137400126

Author: Raymond Barnett, Michael Ziegler

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Differential Equations

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Chapter 11.1, Problem 35E

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To discuss: The validity of the statement “If f is a continuous increasing function on [0,∞) such that f(x)>0 for all x, then ∫0∞f(x)dx diverges”.

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Chapter 11.1, Problem 34E

Chapter 11.1, Problem 36E

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Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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The validity of the statement “If f is a continuous increasing function on [ 0 , ∞ ) such that f ( x ) > 0 for all x , then ∫ 0 ∞ f ( x ) d x diverges”.

Solution Summary: The author explains the validity of the statement "If f is a continuous increasing function on left[0,infty

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To discuss: The validity of the statement “If f is a continuous increasing function on [0,∞) such that f(x)>0 for all x, then ∫0∞f(x)dx diverges”.

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Chapter 11 Solutions

The validity of the statement “If f is a continuous increasing function on [ 0 , ∞ ) such that f ( x ) &gt; 0 for all x , then ∫ 0 ∞ f ( x ) d x diverges”.

Solution Summary: The author explains the validity of the statement "If f is a continuous increasing function on left[0,infty

Concept explainers

Videos

To discuss: The validity of the statement “If f is a continuous increasing function on [0,∞) such that f(x)>0 for all x, then ∫0∞f(x)dx diverges”.

Want to see the full answer?

Chapter 11 Solutions

The validity of the statement “If f is a continuous increasing function on [ 0 , ∞ ) such that f ( x ) > 0 for all x , then ∫ 0 ∞ f ( x ) d x diverges”.