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: 66% (3 reviews)
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...
-
In December 2010, the average price of regular unleaded gasoline excluding taxes in the United States was $3.06 per gallon, according to the Energy Information Administration. Assume that the...
-
What Factors Affect the Design of Organizational Structures? (pp. 318324)
-
Information related to plant assets, natural resources, and intangibles at the end of 2012 for Lucy Company is as follows: buildings $1,100,000; accumulated depreciationbuildings $650,000; goodwill...
-
Maryam is interested in investing. There are two options available to her. The annual percentage rate of return is 10% in the first option and the payment is yearly.the annual percentage rate of...
-
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)
-
Cummings Products is considering two mutually exclusive investments whose expected net cash flows are as follows: Construct NPV profiles for Projects A and B. What is each project's IRR? If you were...
-
As part of the study on ongoing fright symptoms due to exposure to horror movies at a young age, the following table was presented to describe the lasting impact these movies have had during bedtime...
-
Exercise 1.10: State space realization Define a state vector and realize the following models as state space models by hand. One should do a few by hand to understand what the Octave or MATLAB calls...
-
Solve: (5)*+1 = 25x
-
The ball bearing made of steel is to be heat treated. It is heated to a temperature of 620C and then quenched in water that is at a temperature of 50C. The ball bearing has a diameter of 5 cm and the...
-
1. Using the net present value? method, calculate the comparative cost of each of the three payment plans being considered by New Med 2. Which payment plan should New Med choose? Explain. 3. Discuss...
-
Omar owns a pickup truck and a moped. He can afford 12 gal of gasoline to be split between the truck and the moped. Omar's truck gets 20 mpg and, with the fuel currently in the tank, can hold at most...
-
Wilsons Auto Repair ended 2011 with Accounts Receivable of $85,000 and a credit balance in Allowance for Uncollectible Accounts balance of $11,000. During 2012, Wilsons Auto Repair had the following...
-
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
-
The company sold merchandise to a customer on March 31, 2020, for $100,000. The customer paid with a promissory note that has a term of 18 months and an annual interest rate of 9%. The companys...
-
imer 2 0 2 4 Question 8 , PF 8 - 3 5 A ( similar to ) HW Score: 0 % , 0 of 1 0 0 points lework CH 8 Part 1 of 6 Points: 0 of 1 5 Save The comparative financial statements of Highland Cosmetic Supply...
-
An investor wants to purchase a zero coupon bond from Timberlake Industries today. The bond will mature in exactly 5.00 years with a redemption value of $1,000. The investor wants a 12.00% annual...
Study smarter with the SolutionInn App