Show that if f: [a, b] R is integrable and g: f([a, b]) R is

Question:

Show that if f: [a, b] → R is integrable and g: f([a, b]) → R is continuous, then g o f is integrable on [a, b]. (Notice by Remark 3.34 that this result is false if g is allowed even one point of discontinuity.)

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

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 04:15 AM

See More Questions

a) Suppose that gn > 0 is a sequence of integrable functions which satisfies Show that if f : [a, b] R is integrable on [a, b], then b) Prove that if f is integrable on [0,1], then tb lim gn (x) dx...
Let f : (0, ) R be differentiable on (0, 1) and assume that f(x) b as x 1. (b) Show that if f(x) a as x , then b = 0. lim (f(x + h)-))ib. lim (f(x)/x) b
Let f : (a, b) R be continuous on [a, b] and differentiable in (a, b). Show that if then f(a) exists and equals A. [Use the definition of f(a) and the Mean Value Theorem.] im f(x)-A
Samples of size n = 5 are collected from a process every half hour. After 50 samples have been collected, we calculate. x = 20.0 and s 1.5. Assume that both charts exhibit control and that the...
Polly Esther Dress Shops Inc. can open a new store that will do an annual sales volume of $837,900. It will turn over its assets 1.9 times per year. The profit margin on sales will be 8 percent. What...
Explain approaches for assessing the return on investment of social media marketing.
Simulate tossing a coin. (a) For a balanced coin, generate 100 flips. (b) For a coin with probability of heads 0.8, generate 100 flips.
From the following, calculate the dividends for common and preferred stock: 8% fully participating preferred stock. The board declared a $210,000 dividend. Preferred stock 5,000 shares, $50 par...
A car company is experiencing a severe parts shortage due to an industrial steel production backlog worldwide. Will it affect the beta of the stock? Explain why or why not.
1. Top Drawer Cleaning CC has received a cheque from one of its customers, in payment of their account. The cheque has two lines across the top left corner, has or bearer crossed out, and has cash...
Prove that (1 - x/k)k e-x uniformly on any closed, bounded subset of R.
Using Theorem 7.10 or Theorem 9.30, prove that each of the following limits exists. Find a value for the limit in each case. a) b) where f is continuously differentiable on [0, 1] and f'(0) > 0. c)...
What are the similarities and differences between a bolt and a rivet? Explain.
According to a survey, 21% of residents of a country 25 years old or older had earned at least a bachelors degree. You are performing a study and would like at least 10 people in the study to have...
E = an odd number. Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose that the outcomes are equally likely. Compute the probability of the event:
Color Blindness The most common form of color blindness is redgreen color blindness. People with this type of color blindness cannot distinguish between green and red. Approximately 8% of all males...
n = 9, p = 0.4, x 3 A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n = 11, p = 0.15, x 4 A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
In the far field of a particular antenna located at the origin, the magnetic field intensity is where I o is the peak value of the input current. Show that the radiation resistance is given by R rad...
10m solution. If Ka(HA) = 10 then pOH of solution will be [Given : log4=0.6] (A) 6.7 (B) Greater than 6.7 & less than 7.0 (C) Greater 7.0 & less than 7.3 (D) Greater than 7.3
Find the cumulative distribution function F and the density function f for each of the random variables R, S, and T in Exercise 12.
Let X be a random variable with cumulative distribution function (a) What is the density function fX for X? (b) What is the probability that X if r < 0, 0, sin (mx/2), if 0Sa <1, 1. F(r) = if 1
Find the generating functions, both ordinary h (z) and moment g (t), for the following discrete probability distributions. (a) The distribution describing a fair coin. (b) The distribution describing...
Solve (2.4 x 10-5) X 875 (2.5 x 107) x (2.8 x 107)
assume there are no outliers. Draw the boxplot for the following frequency table. You may X f rf cf crf 3 7 0.1228 7 0.1228 4 11 0.1930 18 0.3158 5 9 0.1579 27 0.4737 618 6 0.1053 33 0.5789 10 0.1754...
Find the partial derivative of the regularized least squares problem: {) (w + x) (wo + w x ( ) + w x ( ) } + |/\||[w1, w2]|| with respect to wo, w, and w2. Although there is a closed-form solution to...

Show that if f: [a, b] R is integrable and g: f([a, b]) R is

Question:

Step by Step Answer:

Since g is continuous any point of discontinuity ...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions