Let f be the following function on interval [0, 1]x € Qf (x) =l-1 r¢ Q(a) Let Q be the following partition of [0, 1], Q = {0, ,1}, compute U(f, Q), L(f, Q)(b) Prove: Let P = {0 = x0, x1, X2, · * ' , Xn =1} be an arbitarty partition for [a, b], U(f, P) =1, L(f, P) = - 1(c) Prove that ƒ is not integrable on [0, 1].

Answered: Image /qna-images/answer/c9d41465-5958-49b9-a007-f73d04688467.jpg

Let ƒ be the following function on interval [0, 1] x € Q 1-1 x¢Q f (x) = (a) Let Q be the following partition of [0, 1], Q = {0, 3,1}, compute U(f, Q), L(f, Q) (b) Prove: Let P = {0 = x0, x1, X2, • • • , X'n = 1} be an arbitarty partition for [a, b], U(f, P) = 1, L(f, P) = - 1 (c) Prove that ƒ is not integrable on [0, 1].

Let ƒ be the following function on interval [0, 1] x € Q 1-1 x¢Q f (x) = (a) Let Q be the following partition of [0, 1], Q = {0, 3,1}, compute U(f, Q), L(f, Q) (b) Prove: Let P = {0 = x0, x1, X2, • • • , X'n = 1} be an arbitarty partition for [a, b], U(f, P) = 1, L(f, P) = - 1 (c) Prove that ƒ is not integrable on [0, 1].

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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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Let f be the following function on interval [0, 1]
x € Q
f (x) =
l-1 r¢ Q
(a) Let Q be the following partition of [0, 1], Q = {0, ,1}, compute U(f, Q), L(f, Q)
(b) Prove: Let P = {0 = x0, x1, X2, · * ' , Xn =
1} be an arbitarty partition for [a, b], U(f, P) =
1, L(f, P) = - 1
(c) Prove that ƒ is not integrable on [0, 1].

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