Show that F (x, y) = x2 + 3y is not uniformly continuous on the whole plane. Hint: You must prove that there are pairs of points, arbitrarily close together, on which the variation of F is large, for example, (n, 0) and (n + 1/n, 0).

Show that F (x, y) = x2 + 3y is not uniformly continuous on the whole plane. Hint: You must prove that there are pairs of points, arbitrarily close together, on which the variation of F is large, for example, (n, 0) and (n + 1/n, 0).

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

See similar textbooks

Related questions

Q: Evaluate the integral. z dx dy da W is the region bounded by the planesx0, y 0,0, z-1, and the…

A: Evaluation of the triple integrals, uy conversion of cylindrical coordinates

Q: Suppose you deposit $2,500 in a CD paying 8% interest, compounded every other month. How much will…

A: Given that Suppose you deposit $2,500 in a CD paying 8% interest, compounded every other month. To…

Q: Rewrite the 2nd order ODE to 1st order ODE. O" = -0.

A: Introduction: A second order linear differential equation can be converted into first order…

Q: For the vector fleid G = (ye +3 cos(3z + y))i + (ze + cos(3r + y))j. tind the Iine integral of G…

Q: True or false: 7. The points of inflection are found by solving the first derivative equal to Zero…

A: 7. no, points of inflections are not found by solving first'order derivative, it's by finding second…

Q: Let y' = -(1- y/k) where k > 0. If y(0) > k/2 and y(0) + k then lim,0 y(t) = k A. true B. false

Q: How many solutions are there to the equation x1 + x2 +3 + x4 + x5 = 39, where each x; is an integer…

A: Solution

Q: Find the (a) true error and (b) relative error of the following: The derivative of f(x) = 2^(−x) at…

A: here we use the approximate and exact formula of derivative.

Q: Given the power series E n A, xlu - 1) n =1 Use the technique that we covered in this lesson to…

A: Introduction: When an infinite series is expressed in the form of ∑n=0∞anxn, the series is referred…

Q: Solve the initial value problem y" – y = cos(x) with y(0) = 0 and y (0) = 1.

A: Given differential equation is y'' - y = cos(x) with y(0) = 0 and y'(0) = 1

Q: ) Solve the initial value problem y" + 4y' + 4y = 8xe-2 where y(0) = 1 and y'(0) = -2.

Q: ) Find the exact Sum of the following అఅయా 47.(and! series 25 A, 2. D-1

Q: Show that the following first order differential equation is exact, and then find the general…

Q: Answer the following. 1. Find x if 2x309 is divisible by 9 2 Find the canonical prime factorization…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Find the radius of convergence, R, of the series. (x – 9)^ n=1 R= Find the interval, I, of…

A: Interval of convergence and radius of convergence

Q: Find the values of p for which the series is convergent. (Enter your answer as an inequality.) En°(1…

Q: 7-3 Exam Two The eamhas 12 quetons and you are eured to provide epanatons of your soutonstoeach…

Q: Find the mass of the solid with density p(x, y, 2) and the given shape. P(x, y, z) - 48, solid…

A: Mass of the solid

Q: Find a power series representation for f(x) 1+x3° By differentiating the power series obtained in…

Q: Q1. Solve the following linear ODES/IVPS. 1 dx а. 1 cost = cost, - х dt х dy t dt + 2y = 4e4t ;y(0)…

Q: Find all solutions to the equation (D^2 − 3D + 2)y(x) = 2e^3x.

Q: ses weight by exercising is directly proportional to is/her current weight at time t if certain…

Q: R(x.y) = 25x + 65y +0.07xy – 0.02x2-0.01y², C(x.y)=3x +2y + 200 e the first order partial derivative…

A: P=R-C P(x,y)=R(x,y)-C(x,y) P(x,y)=25x+65y+0.07xy-0.02x2-0.01y2-(3x+2y+200)…

Q: How many unique 5 card hands can be drawn from a deck of cards? (A hand would be formed by drawing…

A: A deck of card has 52 cards. Now we can draw 1st card in 52 ways. Each of these 52 ways we can draw…

Q: Зх — 2у + 3)с

Q: Find a basis for the column space of 3 4 2 3 4 2 -1 A = -3 -4 -1 -3 -5 -12 2 -5 -10 Basis

Q: Exercise 14.4.22. Let o be a permutation in S„. (a) Show that there exists an integer k > 1 such…

A: Please post the multiple parts separately.Here I answered 1st three sub-parts as per our policy.

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below.…

A: We have to solve by Laplace transform method.

Q: 23. Let A be a non-empty set of positive numbers, which is bounded above and let B = {xe R: 1/xe A}.…

Q: Construct proofs to show that the following symbolic arguments are valid. Commas mark the breaks…

Q: Given: f(x) x2 with f'(x) = 4' x²(x² – 12) (x² – 4)² 8x(x² + 12) (x² – 4)3 ° and f"(x) = (a) Find…

A: As per our guidelines we need to solve only three subparts. Please, repost the remaining subparts as…

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. 5, t…

Q: Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the…

Q: Construct proofs to show that the following symbolic arguments are valid. Commas mark the breaks…

Q: What are the dimensions for the cheapest possible rectangular box with a volume of 396 cm3 if the…

Q: Find the solution of the differential equation x In x = y(1+ /3 + y2 )y' that satisfies the initial…

Q: Use substitution method

Q: Use the fact that matrices A and B are row-equivalent. 1 2 10 2 5 1 1 2 2 -2 A = 3 7 19 44 13 4 4 3…

A: As per bartleby guidelines we are supported to answer only first three subparts. Kindly repost rest…

Q: ExeraiSE 4Let the Open set dEnse 5- YOVE metrc Space Cs,d) Hen in

Q: EXAMPLE 5 Show that the vector field F(x, y, z) = xz²i + x?yz®j - y*k can't be written as the curl…

Q: For the vector fleid G = (ye +3 cos(3r + y)) i + (ze + cos(3r + v)) j, tind the line integral of G…

Q: iven: In(1+x) = Σ n +1 (-1)" if |a| < 1. n=0 Find the Maclaurin series for f(x) = x ln (1+ 5).

A: Macluarin series of the function

Q: Q/ Use the Piting method for the table blow:- 3. 4. 12 27 48 Find numerically the Fit equation. by…

Q: Theorem: (i) If Fa is a closed set for each a er then Fa is closed. aer (ii) If Fk is a closed set…

Q: A. (CHAPTER 6) Suppose there are two islands. The total population on the two islands is 800 people.…

Q: d"F (t) = (-t) f(t), where f=£{F}. Use this equation to compute £'(F}. One property of Laplace…

A: Given- One property of Laplace transforms can be expressed in terms of the inverse Laplace transform…

Q: in how many different ways can 7 potted plants be arrangesd in row

A: We can arrange n things in n! ways in a row.

Q: (a) Find dy – Ay, if y = 6–- 7x (b) Find the derivative of f(x) = 2(cos4x – sin4x) Solution.

Q: Find the exact value of sin 0+ cos 0 if cos 0- 23 sin 0=13 and 180° <0<270°. ... sin 0+ cos 0 =…

Q: [1 0 -3 T-4 9. 37 Show that A = 1 3 and B = |-4 8 2 are similar matrices by finding an invertible…

A: First we'll find eigen value and eigen vectors of matrices A and B. For matrix B

Question

Show that F (x, y) = x2 + 3y is not uniformly continuous on the whole plane.
Hint: You must prove that there are pairs of points, arbitrarily close together, on which the
variation of F is large, for example, (n, 0) and (n + 1/n, 0).

Expert Solution