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....
-
a. Show that the solution of the equation is b. Then use the initial condition i(0) = 0 to determine the value of C. This will complete the derivation of Equation (7). c. Show that i = V/R is a...
-
What made you want to become a fashion buyer? LO.1
-
Forester Company has five products in its inventory. Information about the December 31, 2018, inventory follows. The cost to sell for each product consists of a 15 percent sales commission. The...
-
You are planning a new project that is to be entirely financed by issuing new debt. The project will require $ 19.18 million in financing and you estimate its NPV to be $ 15.685 million. The issue...
-
Consider the data set of paving slab weights given in DS 6.1.7. The slabs are supposed to have an average weight of 1.1 kg. Is there any evidence that the manufacturing process needs adjusting?...
-
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 ...
-
What did the automotive supplier certification expert typically see in his experiences?
-
int rFibNum(int a, int b, int n) { if(n == 1) return a; else if( n == 2) return b; else return rFibNum(a,b, n-1) + rFibNum(a, b, n-2); } In the code above; a) how many base cases are there? b) what...
-
Watch the Super Nanny (i.e., Jo Frost) episode "The Orm Family" (Season 1, Episode 3) and answer the following questions. Unless otherwise specified, your answers should focus on Declan (the 3 year...
-
2. Suppose Ford officials were asked to justify their decision. What moral principles do you think they would invoke? Assess Ford's handling of the Pinto from the perspective of each of the moral...
-
2. You have been asked to design the proto-type of an Automatic Grocery Vending Machine 10 (AGVM) for the super store. Automatic Grocery Vending Machine (AGVM) is a machine where different types of...
-
1. What does Porter's 5 Forces analysis strategy do? 2. Do most people agree Why? or disagree with this aspect Why? Here is the reference video, https://www.youtube.com/watch?v=Dfp23xSqpdk 3. What...
-
What is a Named query and why is it used?
-
Refer to the table to answer the following questions. Year Nominal GDP (in billions) Total Federal Spending (in billions) Real GDP (in billions) Real Federal Spending (in billions) 2000 9,817 578...
-
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
-
3 . Accounting.. How does depreciation impact financial statements, and what are the different methods of depreciation?
-
NEED THIS EXCEL TABLE ASAP PLEASE!!!! Presupuesto Operacional y C lculo del COGS Ventas Proyectadas: Ventas Proyectadas: $ 4 5 0 , 0 0 0 Precio por unidad: $ 4 5 0 Unidades vendidas: 4 5 0 , 0 0 0 4...
-
The wash sale rules apply to disallow a loss on a sale of securities_______? Only when the taxpayer acquires substantially identical securities within 30 days before the sale Only when the taxpayer...
Study smarter with the SolutionInn App