1. In this problem, you'll look at the series 1 One can visualize this series as area, by drawing a k5/4 * k=10 box of area 1o5/4, a box of area 15/4 and so on. (a) There are two ways to draw the series (as boxes) in question. Draw each of them together with the graph y = , on two different graphs. 25/4 (b) Use the picture to write an inequality comparing > 1 to an improper integral. Check the k5/4 k=10 bounds of your improper integral carefully, and be sure you are comparing on the same domain. (c) Is the improper integral you wrote in (b) convergent or divergent? Explain. (d) Using the inequality you wrote in (b) and your answer to (c), what (if anything) can you conclude 1 about the convergence of >, k5/4 k=10 (e) Repeat (b)-(d) with your second picture.
1. In this problem, you'll look at the series 1 One can visualize this series as area, by drawing a k5/4 * k=10 box of area 1o5/4, a box of area 15/4 and so on. (a) There are two ways to draw the series (as boxes) in question. Draw each of them together with the graph y = , on two different graphs. 25/4 (b) Use the picture to write an inequality comparing > 1 to an improper integral. Check the k5/4 k=10 bounds of your improper integral carefully, and be sure you are comparing on the same domain. (c) Is the improper integral you wrote in (b) convergent or divergent? Explain. (d) Using the inequality you wrote in (b) and your answer to (c), what (if anything) can you conclude 1 about the convergence of >, k5/4 k=10 (e) Repeat (b)-(d) with your second picture.
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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Transcribed Image Text:1. In this problem, you'll look at the series >
1
)J: One can visualize this series as area, by drawing a
k5/4 *
k=10
box of area 103/4, a box of area 134 and so on.
115/4
(a) There are two ways to draw the series (as boxes) in question. Draw each of them together with
the graph y=
34 on two different graphs.
x5/4
(b) Use the picture to write an inequality comparing >)
1
to an improper integral. Check the
k5/4
k=10
bounds of your improper integral carefully, and be sure you are comparing on the same domain.
(c) Is the improper integral you wrote in (b) convergent or divergent? Explain.
(d) Using the inequality you wrote in (b) and your answer to (c), what (if anything) can you conclude
1
:?
about the convergence of 2
k5/4
k=10
(e) Repeat (b)-(d) with your second picture.
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