Question: Let p >0 be fixed, and define for (x; y)=/(0; 0)f(x; y)= j xjp/2 j yjj xjp +j yjp ; where is a real parameter.

Let p >0 be fixed, and define for (x; y)=/(0; 0)f(x; y)= j xjp/2 j yjj xjp +j yjp ; where is a real parameter. (i) Prove that lim(x;y)!(0;0)f(x; y)=0(hence ffis continuous at (0; 0) if we set f(0;0)=0 whenever > p/2.(ii) Prove the limit does not exist when p/2.(Conclude in particular there is no choice of f(0; 0)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

For monotone functions f, f0: P Q between posets (P, vP ) and (Q, vQ), let f v f(i) Prove that the binary relation v is a partial order. [3 marks] (ii) For monotone functions between posets p : P 0...

hi I need those questions about the estimate of cost of capital and expansion scenario answered as soon as possible please thank you for your help -- - ---- - - -- - - -- - - - - - - - - --- --- i)...

hi I need those questions about the estimate of the cost of capital and expansion scenario answered as soon as possible please thank you for your help hi I need those questions about the estimate of...

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

1 Multivariable functions and vector geometry Due date and time: Wednesday, June 7th at 9:30 AM in lecture Please ensure that you have read and understood the document \"Homework Guidelines" on the...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

ttth Suppose that the sequence of bags {Bn | n N} is recursively enumerated by the computable function e(n, x) = fn(x), [7 marks] Hence prove that the set of all recursive bags cannot be recursively...

Give Correct ANSWERS Human-Computer Interaction (a) If you had been one of the original inventors of the WIMP interface, and engineers on the technical team had been sceptical about the advantages...

2) Suppose X, X2, ..., Xn are independent and identically distributed random variables s.t, E(X) = ne and Var (X) = 20; i = 1,2,.., n. Let T = X/n(n + 16) be an estimator for 0. Show that T is...

Flow around a 90 corner can be modeled with a complex potential a) High-Re flow would actually have a hard time turning that corner. Describe qualitatively, with a picture, what the actual flow...

The implied cost of equity capital has been used as a popular proxy for expected stock returns in recent years. 1 ) Describe and explain the implied cost of capital. 2 ) Demonstrate how the implied...

Monsoon Inc. is considering bidding on a government project. To do the project, the company must make an initial investment of $9 million to purchase the necessary equipment. The project will last...