Prove that is not differentiable at (0, 0). (x, y) = (0, 0)

Question:

Prove that

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

Let be a continuous real-valued function on the unit circle {x R2 : |x| =1} such that f (0, 1) = g(1, 0) = 0 and g(- x )= - g(x). Define f: R2R by F (x) = {|x| . g (x/|x| x 0, 0 x = 0. (a) If x R2...
Let (a) Show that f is continuous at 0. (b) Investigate graphically whether f is differentiable at by zooming in several times toward the point (0, 1) on the graph of f. (c) Show that f is not...
Prove that f(x, y) = |x, y| is not differentiable at (0, 0).
Segment Analysis Winston Sylvester Corporation is a brokerage and financial service company. The company recently provided information about its major business segments as follows (in millions):...
Mr. John Hailey has $1,000 to invest in the market. He is considering the purchase of 50 shares of Comet Airlines at $20 per share. His broker suggests that he may wish to consider purchasing...
Earlier you met two members of the Public Relations Clubs executive committee: Wade and Rhea. Now lets meet three other members: Sonya, Bob, and Eric. Each of these members has his or her own...
Show that the two-sided p-value is $1-\hat{F}_{T}\left(\left|t^{*} ight| ight)+\hat{F}_{T}\left(-\left|t^{*} ight| ight)$, where $\hat{F}_{T}$ is the ECDF of the randomization distribution of...
(Adjusting Entries and Financial Statements) Yount Advertising Agency was founded by Thomas Grant in January 2001. Presented below are both the adjusted and unadjusted trial balances as of December...
For example, if you have two objects, one with weight 5 and one with weight 7, you can measure items of weight 5, 7, or 12. You can also measure items of weight 2, by placing 7 on one side and 5 on...
Beds and Spreads Inc. specializes in bed and bath furnishings. Its inventory system is linked through the company's website to key suppliers. The auditor identified the following internal controls in...
Suppose that f, g: R Rm are differentiable at a and there is a Î´ > 0 such that g(x) 0 for all 0 lim
Prove that is differentiable on R2 for all a f(x, y) = Itx2+y2)" (x, y)(0.0) 0
The tire on this drag racer is severely twisted: The force of the road on the tire is quite large (most likely several times the weight of the car) and is directed forward as shown. Is the car...
With regard to conjugation, a key difference between F+ and Hfr cells is that an Hfr cell a. is unable to conjugate. b. transfers a plasmid to the recipient cell. c. transfers a portion of the...
Which of the following statements is correct? a. If a deletion and a duplication are the same size, the deletion is more likely to be harmful. b. If a deletion and a duplication are the same size,...
A cow with scurs and a bull with no scurs have an offspring. This offspring could be a. a female with scurs or a male with scurs. b. a female with no scurs or a male with scurs. c. a female with...
In the experiment by Bateson and Punnett, which of the following observations suggested genetic linkage in the sweet pea? a. A 9:3:3:1 ratio was observed in the F2 offspring. b. A 9:3:3:1 ratio was...
According to the selfish DNA hypothesis, TEs exist because a. they offer the host a selective advantage. b. they have characteristics that allow them to multiply within the chromosomal DNA of living...
The standard deviation of a continuous random variable X can be negative. Determine whether each statement is true or false, and explain why.
How has the globalization of firms affected the diversity of their employees? Why has increased diversity put an additional burden on accounting systems?
Heat treating is often used to carburize metal parts, such as gears. The thickness of the carburized layer is considered a crucial feature of the gear and contributes to the overall reliability of...
Statistics for 21 National Hockey League teams were obtained from the Hockey Encyclopedia and are shown in Table 12-8. The variables and definitions are as follows: Wins Number of games won in a...
Consider the linear regression model where and where x1 = xi1/n and x2 = xi2/n. (a) Write out the least squares normal equations for this model. (b) Verify that the least squares estimate of the...
A restaurant has fixed costs of $ 1 3 2 . 5 0 per day and an average unit cost of $ 4 . 7 5 for each meal served. If a typical meal costs $ 6 , how many customers must eat at the restaurant each day...
A machine to manufacture fasteners has a setup cost of $ 1 , 4 0 0 and a unit cost of $ 0 . 0 0 3 for each fastener manufactured. A newer machine has a setup cost of $ 1 , 7 5 0 but a unit cost of...
K Tom owns a four-sided lot that lies between two parallel streets. If the lot is 120,000-ft2 and has 500 ft frontage on one street and 300 ft frontage on the other, then how far apart are the...

Prove that is not differentiable at (0, 0). (x, y) = (0, 0)

Question:

(x, y) = (0, 0)

Step by Step Answer:

By definition Thus the first part...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions