|1, når 0 0 there is partition Pe of [0,1] so that for the lesser Riemann sum L(f, P.) holds true that L(f, P.) > i – e. b) Use (a) to show that fis integrable and that S f(x)dr = 1. %3D c) Let g be a decreasing continuous function of [0,1] which presumes the values g(0)=1 and g(1)=0. Show that there is a Partition P of [0,1] so that the following inequalities holds true for the lower and the higher Niemann sum. 0 < L(g, P) < U(9, P) < 1 d) Use (c) to show the inequalities: < / g(x)dx < 1.
|1, når 0 0 there is partition Pe of [0,1] so that for the lesser Riemann sum L(f, P.) holds true that L(f, P.) > i – e. b) Use (a) to show that fis integrable and that S f(x)dr = 1. %3D c) Let g be a decreasing continuous function of [0,1] which presumes the values g(0)=1 and g(1)=0. Show that there is a Partition P of [0,1] so that the following inequalities holds true for the lower and the higher Niemann sum. 0 < L(g, P) < U(9, P) < 1 d) Use (c) to show the inequalities: < / g(x)dx < 1.
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
100%
![e Vol) 4G
LTE1
ll 39% Ô 9:26 PM
You
5 minutes ago
a) Let the function fbe given by:
[1, når 0 <x < 1,
f(x) =
| 0, når x = 1.
Show that for each € >0 there is partition
Pe
of [0,1] so that for the lesser Riemann sum
L(f, P.)
holds true that L(f, Pc) > 1 –
- E.
b) Use (a) to show that fis integrable and that
So f(x)dr = 1.
c) Let g be a decreasing continuous function of
[0,1] which presumes the values g(0)=1 and
g(1)=0. Show that there is a Partition P of [0,1]
so that the following inequalities holds true for
the lower and the higher Niemann sum.
0 < L(g, P) < U(g, P) < 1
d) Use (c) to show the inequalities:
0 <
| g(x)dx < 1.
...](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a516774-86b2-4e24-8c8f-aacc06459ee3%2F43c24716-2738-4985-b06f-b821186168db%2Fie8bmzl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:e Vol) 4G
LTE1
ll 39% Ô 9:26 PM
You
5 minutes ago
a) Let the function fbe given by:
[1, når 0 <x < 1,
f(x) =
| 0, når x = 1.
Show that for each € >0 there is partition
Pe
of [0,1] so that for the lesser Riemann sum
L(f, P.)
holds true that L(f, Pc) > 1 –
- E.
b) Use (a) to show that fis integrable and that
So f(x)dr = 1.
c) Let g be a decreasing continuous function of
[0,1] which presumes the values g(0)=1 and
g(1)=0. Show that there is a Partition P of [0,1]
so that the following inequalities holds true for
the lower and the higher Niemann sum.
0 < L(g, P) < U(g, P) < 1
d) Use (c) to show the inequalities:
0 <
| g(x)dx < 1.
...
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