(b). Answer the True/False questions in Crowdmark. i) xP-7 is convergent when p< 6 ii) If f is continuous on [0, 00), and , f(x)dx is convergent, then f (x)dx is convergent. iii) If f(x) < g(x), and g(x)dx is divergent, then “ f(x)dx also diverges. iv) If fis a continuous, decreasing function on [1, 00) and lim,o f(x) = 0, then f(x)dx is convergent.
(b). Answer the True/False questions in Crowdmark. i) xP-7 is convergent when p< 6 ii) If f is continuous on [0, 00), and , f(x)dx is convergent, then f (x)dx is convergent. iii) If f(x) < g(x), and g(x)dx is divergent, then “ f(x)dx also diverges. iv) If fis a continuous, decreasing function on [1, 00) and lim,o f(x) = 0, then f(x)dx is convergent.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please only do part (b)
Transcribed Image Text:Q1(a).Use integration, and the methods covered in this course (Comparison Theorem (CT),
and or Limit Comparison Test(LCT)), to test the integral for convergence:
dx
(b). Answer the True/False questions in Crowdmark.
i) xP-7 is convergent when p < 6
ii) If f is continuous on [0, 00), and S," f(x)dx is convergent, then " f(x)dx is convergent.
iii) If f(x) < g(x), and S g(x)dx is divergent, then f(x)dx also diverges.
iv) If fis a continuous, decreasing function on [1, 0) and limx»of(x) = 0, then f, f(x)dx is
convergent.
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