6. Are the following statements true or false? If true explain, if false give a counter example.(a) For any function f(x), f(z) dr = lim f(x) d.r.(b) If lim f(r) = 0 and f(r) dr converges absolutely, thenSu)*dr converges.(c) If | f(x) dr diverges, then/(s(#})* dæ converges by the limit comparison test.(d) If / f(x) dr andg(x) dr are both divergent, then(f(x) + g(x)) da is divergent.a

Answered: Image /qna-images/answer/71026b68-0c99-4d90-a822-b47c7d60975d.jpg

6. Are the following statements true or false? If true explain, if false give a counter example. (a) For any function f(x), f(r) dr = lim f(z) dz. (b) If lim f(r) = 0 and f(z) dz converges absolutely, then /(f(z))* dr converges. (c) If (x) dr diverges, then (S)* dr converges by the limit comparison test. (d) If / f(x) dr and / 9(r) dr are both divergent, then / (S(x) + g(x)) dr is divergent.

6. Are the following statements true or false? If true explain, if false give a counter example. (a) For any function f(x), f(r) dr = lim f(z) dz. (b) If lim f(r) = 0 and f(z) dz converges absolutely, then /(f(z))* dr converges. (c) If (x) dr diverges, then (S)* dr converges by the limit comparison test. (d) If / f(x) dr and / 9(r) dr are both divergent, then / (S(x) + g(x)) dr is divergent.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

6. Are the following statements true or false? If true explain, if false give a counter example.
(a) For any function f(x), f(z) dr = lim f(x) d.r.
(b) If lim f(r) = 0 and f(r) dr converges absolutely, then
Su)*dr converges.
(c) If | f(x) dr diverges, then
/(s(#})* dæ converges by the limit comparison test.
(d) If / f(x) dr and
g(x) dr are both divergent, then
(f(x) + g(x)) da is divergent.
a

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