Let f(x) = xe-2² be defined on [1, 0) and let a,n = f(n) for positive integers n. (i) Examine why the Integral Test can be used to determine the convergence of the series E-1 an. n%=D1 (ii) By using the Integral Test, determine the convergence of E, an: (iii) Hence, deduce the limit limn-0 an. Give your reason. (iv) Does Ln=1 an converge absolutely? Justify your answer.
Let f(x) = xe-2² be defined on [1, 0) and let a,n = f(n) for positive integers n. (i) Examine why the Integral Test can be used to determine the convergence of the series E-1 an. n%=D1 (ii) By using the Integral Test, determine the convergence of E, an: (iii) Hence, deduce the limit limn-0 an. Give your reason. (iv) Does Ln=1 an converge absolutely? Justify your answer.
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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