Question: Give an example of a function of two variables defined on the unit disk in plane which admits Directional Derivatives in every direction in the

Give an example of a function of two variables defined on the unit disk in plane which admits Directional Derivatives in every direction in the \( x y \)-plane around the origin, but does not admit an overall derivative, thus, is not differentiable at the origin. Prove your claim in detail.

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!

Q:

Give an example of a function of two variables defined on the unit disk in plane which is class \ ( \ mathrm { C } ^ { \ wedge } 1 \ ) but is not \ ( \ mathrm { C } ^ { \ wedge } 2 \ ) . Justify your...

Q:

Q2 [4]. Functions, derivatives, gradients Consider a function of two variables y = f(x1, x2) = 4(x1 - 1)2 + 3(x2 - 2)2. The function represents a surface in the three-dimensional space (C1, 12,y)....

Q:

H f(x,x) g(s). .......s , 7. Q2 [4]. Functions, derivatives, gradients Consider a function of two variables y = f(x1, x2) = 4(x1 - 1)2 + 3(x2 - 2)2. The function represents a surface in the...

Q:

Calculus 3 Section 14.5 Reading Assignment: Directional Derivatives and Gradient Vectors I am suck with this question. Please help! Section 14.5 Reading Assignment: Directional Derivatives and...

Q:

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

Q:

Suppose that R(A, B, C) is a relational schema with functional dependencies F = {A, B C, C B}. (i) Is this schema in 3NF? Explain. [2 marks] (ii) Is this schema in BCNF? Explain. [2 marks] (b)...

Q:

Prolog You are approached to compose a Prolog program to work with twofold trees. Your code shouldn't depend on any library predicates and you ought to expect that the mediator is running without...

Q:

re Regular Languages and Finite Automata (a) Let L be the set of all strings over the alphabet {a, b} that end in a and do not contain the substring bb. Describe a deterministic finite automaton...

Q:

ANSWER. THESE QUESTIONS AS GIVEN IN THE ATTACHMENT. (a) Use implicit differentiation to compute and where z is defined implicitly by y . cos(I' 2) = 1. [3 marks] (b) Suppose that a function f(r, y)...

Q:

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...

Q:

How would you carry out these transformations? OH . b. from HO, and

Q:

A homeowner is currently using a natural gas furnace for heating the house in winter but he is considering replacing this system with a furnace burning wood pellets. The homeowner currently pays an...

Q:

Net operating profit after taxes ( NOPAT ) is defined as which of the following? 1 0 pointsMultiple Choice 0 7 . 3 9 . 0 0 net profit a firm earns before taxes, and before any financing costnet...

Q:

A particle is moving in three dimensions and its position vector is given by; r(t) = (4, 4t + 2, 3t)i + (4, 5t - 2, 3)2 + (3, 3t + 3, 1t)k where r is in meters and t is in seconds. Determine the...