Let f(x) = 0 if is any rational number and f(x) = 1 if is any irrational

Question:

Let f(x) = 0 if is any rational number and f(x) = 1 if is any irrational number. Show that f is not integrable on [0, 1]

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0538497909

7th edition

Authors: James Stewart

See More Books

Question Posted: Mar 04, 2016 06:56 AM

See More Questions

Let f (x) = 0 if x is any rational number and f (x) = 1 if x is any irrational number. Show that f is not integrable on [0, 1].
Let f(x + y) = f(x) + f(y) for all x and y. Prove that there is a number in such that f (t) = nit for all rational numbers t.
Let f : R R and let f (x) > 0 for all x R. Show that f (x) is strictly decreasing if and only if the function g(x) = 1/f (x) is strictly increasing.
MULTIPLE CHOICE: 6. The stage of production at which the individual jointproducts are identified is referred to as the: A. Split-off point B. Joint point C. Separate identification point D. Relative...
ABC Inc. engaged in the following selected transactions during the year. Identify whether each of 1 through 8 represents an equity investment (E), investment in a debt security (D), or neither (N)...
In a conventional exterior wall, a 2 6 wooden stud is placed every 16 in. (A stud is an upright support.) The stud runs all the way from the exterior siding to the interior wall and the spaces...
Let $p(t)$ be the probability of survival from 0 to $t$. The probability of surviving to $s$ given survival to $t$ is then \[p(s \mid t)=\frac{p(s)}{p(t)}\] Let...
Critics of absorption costing have increasingly emphasized its potential for leading to undesirable incentives for managers. Give an example.
Question 1 Based on the details shared in the video, come up with various criteria based on which Protinex could do segmentation. Additionally, provide your rationale for it. Mention at least three...
On December 31, the capital balances and profit and loss ratios in the MRS Partnership are as follows Capital Profit and Partner Balance loss ratio B. McLaren $106,000 51% P. Ready 93,000 24% D....
Use Property 8 to estimate the value of the integral. a. b. c. tan x dx
A table of values of an increasing function f is shown. Use the table to find lower and upper estimates for /(x) dr. 10 14 18 22 26 30 (x12 8
What part of the damages will Hampton Insurance Company pay on a home with $ 18,000 damage by fire if the replacement COM is $86,000 and it is insured for $65,000? The policy contains an 80%...
You are in charge of planning a new investment for your firm that will cost $850,000 today. The investment is expected to produce a cash flow of $450,000 in year one. Each of the following years the...
1. Some people think that profit maximization should be the goal of finance, where some other students seems Wealth maximization must be the goal of finance. What is your opinion on that? List out 5...
How do you '' sell yourself ''? I mean.... You personally. What do you do that makes you a defining difference maker in the art of sales? Your explanation can be the way you dress, talk, prepare, etc
Explain the different alternatives for short term financing and the criteria applied in the selection process?
The foundation for a cylindrical water tank is a cylinder 27 ft in diameter and 3 ft high. How many cubic ft of concrete are needed to build the foundation?
Describe the various types of control charts and their applications.
What are the key elements of a system investigation report?
Use a graph of the vector field F and the curve C to guess whether the line integral of F over C is positive, negative, or zero. Then evaluate the line integral. F(x, y) = (x - y) i + xy j, C is the...
Use a graph of the vector field F and the curve C to guess whether the line integral of F over C is positive, negative, or zero. Then evaluate the line integral. F(x, y) = x/x 2 + y 2 i + y/x 2 + y 2...
Find the exact value of C x 3 y 2 z ds, where C is the curve with parametric equations x = e 2-t cos 4t, y = e 2-t sin 4t, z = e 2-t , 0 < t < 2.
Discuss the incident response steps and the recovery strategy and phases.
Compare and contrast planning and innovation with citation and references.
How are the tools used for planning, monitoring, and reporting in Six Sigma?

Let f(x) = 0 if is any rational number and f(x) = 1 if is any irrational

Question:

Step by Step Answer:

Suppose that f is integrable on 0 1 that is Exists for any ...View the full answer

Calculus Early Transcendentals

Students also viewed these Calculus questions