Prove that is continuous on R2 and has first-order partial derivatives everywhere on R2, but f is

Question:

Prove that

is continuous on R2 and has first-order partial derivatives everywhere on R2, but f is not differentiable at (0, 0).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 04:19 AM

See More Questions

Prove that is not differentiable at (0, 0). (x, y) = (0, 0)
Prove that f(x, y) = |x, y| is not differentiable at (0, 0).
(a) Recall (Sec. 5) that if z = x + iy, then By formally applying the chain rule in calculus to a function F(x, y) of two real variables, derive the expression (b) Define the operator suggested by...
Explain why the coffee shop manager should measure elasticity using the mid-point method in his calculations.
Assume you can buy a warrant for $6 that gives you the option to buy one share of common stock at $14 per share. The stock is currently selling at $18 per share. a. What is the intrinsic value of the...
For a 15-m 20-m one-story house located in San Francisco, CA, determine the cost-effectiveness of retrofit of the windows with SISs. The house has a BLC of 500 W/C, wall height of 3.50 m, and WWR of...
Identify treatments and experimental units in the following scenarios. a. City A would like to evaluate whether a new employment training program for the unemployed is more effective compared to the...
A survey of the business school graduates undertaken by a university placement office asked, among other questions, in which area each person was employed. The areas of employment included: 1....
The Waner Company is trying to do cost - volume - profit analysis with the following information for the month of June. WANER COMPANY INFORMATION FOR PERFORMING COST - VOLUME - PROFIT ANALYSIS FOR...
1. Why do you think Rolls has continued to bear this structural currency mismatch so long? Why hasn't it done what many automobile companies have done, and move some of their manufacturing and...
Prove that if a > 1/2, then is differentiable at (0, 0). ylog(2 y x y) (x, y) (0, 0) (0.0) f(a. y)
Suppose that T (Rn; Rm). Prove that T is differentiable everywhere on Rn with DT(a) = T for a Rn.
Information about Elsa's Boards is presented in E6-4. Additional data regarding Elsa's sales of Xpert snowboards are provided below. Assume that Elsa's uses a perpetual inventory system. Instructions...
What is/are the phenotype(s) of the recombinant offspring of the F2 generation? a. red eyes, long wings b. white eyes, miniature wings c. red eyes, long wings and white eyes, miniature wings d. red...
In mammals, sex is determined by a. the SRY gene on the Y chromosome. b. having two copies of the X chromosome. c. having one copy of the X chromosome. d. both a and c.
The role of cohesin is to a. make chromosomes more compact. b. allow for the replication of chromosomes. c. hold sister chromatids together. d. promote the separation of sister chromatids.
In fruit flies, dosage compensation is achieved by a. X-chromosome inactivation. b. doubling the expression of genes on the single X chromosome in the male. c. halving the expression of genes on each...
An abnormal fruit fly has two sets of autosomes and is XXY. Such a fly is a. a male. c. a hermaphrodite. b. a female. d. none of the abo
An integrating factor turns a linear differential equation into one that can be solved by integrating both sides of the equation. Determine whether each statement is true or false, and explain why.
Explain the term "Equivalent Units". Why are they calculated in process costing? [4 Marks] [minimum 350 words]
Consider the electric power consumption data in Exercise 12-6. (a) Test for significance of regression using a = 0.05. What is the P-value for this test? (b) Use the t-test to assess the contribution...
Consider the bearing wear data in Exercise 12-7 with no interaction. (a) Test for significance of regression using a = 0.05. What is the P-value for this test? What are your conclusions? (b) Compute...
Reconsider the bearing wear data from Exercises 12-7 and 12-20. (a) Refit the model with an interaction term. Test for significance of regression using a = 0.05. (b) Use the extra sum of squares...
A 7 5 kg cliff - diver is falls from a height through the air head, diving towards the water. The drag coefficient for the diver is 0 . 8 3 and the area of the descending diver is 0 . 2 1 m ^ 2 ....
In the automobile industry, the dimensionless drag coefficient and the area of the vehicle are often combined into one variable - the drag area whereby the drag area is the product of the...
When you drop 10 pebbles into the well, you record the times for hearing the splash as 2.94 s, 3.11 s, 3.12 s, 2.97 s, 3.12 s, 2.97 s, 3.06 s, 3.21 s, 3.37 s, and 3.53 s. (a) Find the average time...

Prove that is continuous on R2 and has first-order partial derivatives everywhere on R2, but f is

Question:

(x, y)关(0.0) (x, y) = (0,0) f(x, y) = X2 +y2 0

Step by Step Answer:

Clearly f is continuous and has firstorder partial derivatives at every point x y 0 ...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions