Let (x, y) = xy/(x 2 + y 2 ). Show that (x, y) approaches zero along
Question:
Let ƒ(x, y) = xy/(x2 + y2). Show that ƒ(x, y) approaches zero along the x- and y-axes. Then prove that does not exist by showing that the limit along the line y = x is nonzero.
Transcribed Image Text:
lim f(x,y) (x,y) (0,0)
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (QA)
Case 1 Consider the limit along the xaxis y 0 xy lim xy00 x y 0 lim x0x 0 Case 2 ...View the full answer
Answered By
Fahmin Arakkal
Tutoring and Contributing expert question and answers to teachers and students.
Primarily oversees the Heat and Mass Transfer contents presented on websites and blogs.
Responsible for Creating, Editing, Updating all contents related Chemical Engineering in
latex language
4.40+
8+ Reviews
22+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Show that the limit does not exist by approaching the origin along one or more of the coordinate axes. x - y+z lim (xyz) (0,0,0) x2 + y + z
-
Show that the limit does not exist by approaching the origin along one or more of the coordinate axes. x+y+z lim 2 (x,y,z) (0,0,0) x + y + z
-
According to the WLLN (Application 1 to Theorem 9), if the r.v.s X 1 ,...,X n are i.i.d. with finite X 1 , then The following example shows that it is possible for {S n /n} to converge in probability...
-
What effect does a weakening in U.S dollar have on Net Income for subsidiaries of U.S companies?
-
(Issuance and Retirement of Bonds; Income Statement Presentation) Holiday Company issued its 9%, 25-year mortgage bonds in the principal amount of $3,000,000 on January 2, 1996, at a discount of...
-
A crystal of salt consists of negative and positive ions. How does the net charge of the negative ions compare with that of the positive ions? Explain.
-
Define the differences between a sales forecast and a market forecast.
-
In 2012, Grissom Company had a break-even point of $350,000 based on a selling price of $7 per unit and fixed costs of $105,000. In 2013, the selling price and the variable cost per unit did not...
-
As part of a school science fair, students from various school districts must be transported to the various locations. School districts are as follows (with the number of attendees listed by...
-
Let Set y = mx and show that the resulting limit depends on m, and therefore the does not exist. f(x,y) = 2x + 3y
-
Assume that to find the limit. lim f(x, y) = 3, (x,y)-(2,5)* lim g(x,y) = 7 (x,y)-(2,5)
-
Find the real values of x satisfying the following equations. a. x 4 5x 2 + 4 = 0 b. x 4 + x 2 6 = 0 c. x 4 20x 2 + 64 = 0 d. x 4 + 2x 2 8 = 0 e. x 4 4x 2 21 = 0 f. 2x 4 17x 2 9 = 0 g. 4x 4 +...
-
Draw a diagram of the market for oranges. Explain how the government policy you discussed in part (b) of Problem 5-2 is likely to affect the market price and equilibrium quantity in the orange...
-
The intensity level at the front of a library reading room is \(70 \mathrm{~dB}\) when 120 students are in the room and \(20 \mathrm{~dB}\) when the room is empty. What do you expect the intensity...
-
A hollow stirrer that has a diameter of \(1.0 \mathrm{~mm}\) is inserted into a cup of water at \(20^{\circ} \mathrm{C}\). The surface tension of water at that temperature is \(\gamma=7.28 \times...
-
A 55 g soapstone cubea whisky stoneis used to chill a glass of whisky. Soapstone has a density of 3000 kg/m 3 , whisky a density of 940 kg/m 3 . What is the approximate normal force of the bottom of...
-
Explain the difference between exogenous and endogenous variables.
-
Presented below is information related to radios for the Singles Company for the month of March. Instructions (a) Assuming that the periodic inventory method is used, compute the inventory cost at...
-
Suppose the spot and six-month forward rates on the Norwegian krone are Kr 5.78 and Kr 5.86, respectively. The annual risk-free rate in the United States is 3.8 percent, and the annual risk-free rate...
-
Graph each equation of the system. Then solve the system to find the points of intersection. x + y? = 16 x 2y = 8
-
Graph each equation of the system. Then solve the system to find the points of intersection. %3 4 2 + ? 3D 8
-
Graph each equation of the system. Then solve the system to find the points of intersection. Sx = *y = 1
-
1. Now we consider one single person with x = 0.4. (15') (a) What is the maximum amount she is willing to pay for a health insurance policy that covers the medical treatment in full, if she is...
-
Analyze and illustrate graphically (Draw graph ) the impact of the following events on the market for young palm tree plants at a nursery. Determine the effect on equilibrium price and quantity. In...
-
How does the neuroendocrine axis regulate the stress response, encompassing the hypothalamic-pituitary-adrenal (HPA) axis and the sympathetic-adrenal-medullary (SAM) system, and what are the...
Study smarter with the SolutionInn App