A differentiable function f : I R is said to be uniformly differentiable on I := (a,
Question:
Show that if f is uniformly differentiable on I, then fʹ is continuous on I.
Transcribed Image Text:
79-70-10 f(x) -f(y)
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 76% (13 reviews)
Let x y I x y then so that If f is uniformly differentiable o...View the full answer
Answered By
Brown Arianne
Detail-oriented professional tutor with a solid 10 years of experience instilling confidence in high school and college students. Dedicated to empowering all students with constructive feedback and practical test-taking strategies. Effective educator and team player whether working in a school, university, or private provider setting. Active listener committed to helping students overcome academic challenges to reach personal goals.
4.60+
2+ Reviews
10+ Question Solved
Related Book For
Introduction to Real Analysis
ISBN: 978-0471433316
4th edition
Authors: Robert G. Bartle, Donald R. Sherbert
Question Posted:
Students also viewed these Calculus questions
-
Let f, g: R R be twice differentiable. Prove that u(x, y) := f(xy) satisfies and v(x, y) := f(x - y) + g(x + y) satisfies the wave equation; that is, au-yay=0. ax ay - ax20
-
Let f, g: R2 R be differentiable and satisfy the Cauchy-Riemann equations; that is, that hold on R2. u(r, 0) = f(r cos θ, r sin θ) and v(r, θ) = g(r cos...
-
Suppose that f: Rn R and g: Rn Rn are differentiable on Rn and that there exist r > 0 and a Rn such that Dg(x) is the identity matrix, I, for all x Br(a). Prove that there is a function h: Br(a) {a}...
-
Hernandez Company began 2010 with a $120,000 balance in retained earnings. During the year, the following events occurred: 1. The company earned net income of $80,000. 2. A material error in net...
-
The Pillsbury Company maintained an electronic mail communication system. The company repeatedly assured its employees that all e-mail communications on the system would remain confidential....
-
You stand in your yard and hold a battery-powered buzzer that is emitting a frequency of \(560 \mathrm{~Hz}\) as a friend stands next to you. (a) What frequency does your friend hear if you throw the...
-
Describe the conditions of an insurance policy.
-
For fiscal year 2011, Starbucks Corporation (SBUX) had total revenues of $11.70 billion, net income of $1.25 billion, total assets of $7.36 billion, and total shareholders equity of $4.38 billion. a....
-
Marin Company produces two software products ( Cloud - X and Cloud - Y ) in two separate departments ( A and B ) . These products are highly regarded network maintenance programs. Cloud - X is used...
-
Idexo Corporation is a privately held designer and manufacturer of licensed college apparel in Cincinnati, Ohio. In late 2019, after several years of lackluster performance, the firms owner and...
-
Let I := (a, b) and let f : I R be differentiable at c I. Show that for every ε > 0 there exists δ > 0 such that if 0 f(x) f(y) - f'(c) < e.
-
Find the points of relative extrema, the intervals on which the following functions are increasing, and those on which they are decreasing: (a) f(x) := x + 1/x for x 0. (b) g(x) := x/(x2 + 1) for x ...
-
You are trying to decide whether to buy stock in Company X or Company Y. Both companies need $1000 capital investment and will earn $200 in good years (with probability 0.5) and $60 in bad years. The...
-
Now that we have reached the end of our course, you will have the opportunity to create and name your version of leadership style, theory, or philosophy. As you create your leadership concept, take...
-
Separation of duties is important in internal control procedures. Why should responsibility for related transactions be divided among different departments or individuals? Why should the person who...
-
As a construction company "Conet" operating in Melbourne Victoria, write a thorough formal to a labour hire agency enquiring about fees and charges for 1general labour hire or a group of labours for...
-
How can influential leaders harness the power of social media platforms, digital technologies, and online communities to extend their reach, cultivate thought leadership, and shape discourse in the...
-
Power relating to social status is premised on a willingness to "participate"; what might constitute criteria for non-participation, and should we think of this as a powerful instrument? Add...
-
Write interval notation. Then graph the interval. {x-5 x 5} VI
-
TRUE OR FALSE: 1. Banks with a significantly large share of fixed-interest rate home loans are less exposed to interest rate risks. 2. Although Australian banks are pretty big, they are not...
-
Answer true or false for below Exercises. 1. The absolute value of a number is always a positive number. 2. Zero is always less than a positive number. 3. Given the number line is it true that b 6...
-
Graph each integer in the list on the same number line. See Example 2. 1. 7, 5, 2, 0 2. 3, -3, 5, -5, 6 3. 0, 3, 10, 11 4. 0, -7, 3, -6 + -7 -6 5 -4 -3 -2 -1 4 5 6 7 -7 -6 -5 -4 -3 -2 -1 0. 3 4 1. 5....
-
Fill in the chart below 1. 2. Opposite of Number Absolute Value of Number Number -13 90 Absolute Value of Number Opposite of Number Number -13 90
-
How can bash shell scripting improve resource utilization and process management in Unix systems?
-
A solid sphere that is uniformly positively charged produces an electric field. Assume no other objects are around. What is the magnitude of the electric field a distance r from the center of the...
-
Why is potential difference important in x - ray production?
Study smarter with the SolutionInn App