(a) Let 3, f(x) = 2x, 4-2, x=0, 0 < x≤ 2, 2
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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![(a) Let
3,
f(x)=2x,
4-2,
and let P be the partition of [0, 4] given by P = {[0, 1],[1, 2], [2, 4]).
(i) Sketch the graph of f.
(ii) Evaluate L(f,P) and U(f, P).
(b) Prove that
2π
3 (4+√3)
x=0,
0 < x≤ 2,
2<x≤ 4,
/33+2cos
4+2sinx
Σ
<
=√16³ 3
(c) (i) Let p> 1. Show that
|
z(logz)p=1(loga)l-p.
(ii) Hence determine whether the series
1
n(logn)P
is convergent or divergent.
π
da ≤ (1+1/√3).
for p > 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78199da8-8819-492e-ab85-20d0b150b303%2F4c13d3f7-4905-4349-9468-df96d78b2bc6%2Ffeioto2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Let
3,
f(x)=2x,
4-2,
and let P be the partition of [0, 4] given by P = {[0, 1],[1, 2], [2, 4]).
(i) Sketch the graph of f.
(ii) Evaluate L(f,P) and U(f, P).
(b) Prove that
2π
3 (4+√3)
x=0,
0 < x≤ 2,
2<x≤ 4,
/33+2cos
4+2sinx
Σ
<
=√16³ 3
(c) (i) Let p> 1. Show that
|
z(logz)p=1(loga)l-p.
(ii) Hence determine whether the series
1
n(logn)P
is convergent or divergent.
π
da ≤ (1+1/√3).
for p > 1.
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