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These Statements are false, please provide an explicit counterexample: a) If f(x) is a continuous, always positive function on (1,20) and lim F(x) = 0 then S, f(x)dx will converge. b) It an is an always positive sequence and diverges then an∞.

These Statements are false, please provide an explicit counterexample: a) If f(x) is a continuous, always positive function on (1,20) and lim F(x) = 0 then S, f(x)dx will converge. b) It an is an always positive sequence and diverges then an∞.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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These Statements are false, please provide an explicit counterexample: a) If f(x) is a continuous, always positive function on (1,20) and lim F(x) = 0 then S, f(x)dx will converge. b) It an is an always positive sequence and diverges then an∞.
Transcribed Image Text:These Statements are false, please provide an explicit counterexample: a) If f(x) is a continuous, always positive function on (1,20) and lim F(x) = 0 then S, f(x)dx will converge. b) It an is an always positive sequence and diverges then an∞.
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