Consider the function (a) Show that as (x, y) (0, 0) along any line y =

Question:

Consider the function f(x, y) = xy x6 + 2y

(a) Show that as (x, y) → (0, 0) along any line y = mx, the limit equals 0.

(b) Show that as (x, y) → (0, 0) along the curve y = x³, the limit does not equal 0, and hence, lim f(x, y) (x,y) (0,0) does not exist.

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

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Jan 16, 2024 10:00 AM

See More Questions

KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...
For the month ending September 30, 2020, Gardener Company has received $10,000 from customers, $30,000 in capital contributed from shareholders, and borrowed $20,000 from the bank. The company also...
An experiment showed that subjects fed the DASH diet were able to lower their blood pressure by an average of 6.7 points compared to a group fed a "control diet." All meals were prepared by...
A stone is catapulted at time t = 0, with an initial velocity of magnitude 20.0 m/s and at an angle of 40.0 above the horizontal. What are the magnitudes of the (a) Horizontal and (b) Vertical...
FAOSTAT, the Food and Agriculture Organization of the United Nations, collects in-formation on the production and consumption of more than 200 food and agricultural products for 200 countries around...
E19-6 Compute the 20X5 cost of goods manufactured and cost of goods sold for Strike Marine Company using the following amounts: Materials inventory Work in process inventory...... Finished goods...
Western Farms is a producer of items made from local farm products that are distributed to supermarkets. Over the years, price competition has become increasingly important, so Doug Gilbert, the...
Required information [The following information applies to the questions displayed below) Lansing Company's current-year income statement and selected balance sheet data at December 31 of the current...
Compute the given partial derivatives. f(x, y) = sin(x - y), fy(0,7)
Prove that if (x) is continuous at x = a and g(y) is continuous at y = b, then F(x, y) = (x)g(y) is continuous at (a, b).
A couple plans to have 4 children. a. List the 16 different possible outcomes according to the gender of each child. Assume that these outcomes are equally likely. b. Find the probability of getting...
16. List I describes four systems, each with two particles A and B in relative motion as shown in figures. List II gives possible magnitude of their relative velocities (in m s) at time t = 3 S....
17. List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the...
1. 2 mol of Hg(g) is combusted in a fixed volume bomb calorimeter with excess of O2 at 298 K and 1 atm into HgO(s). During the reaction, temperature increases from 298.0 K to 312.8 K. If heat...
3. A solution is prepared by mixing 0.01 mol each of H2CO3, NaHCO3, Na2CO3, and NaOH in 100 mL of water. pH of the resulting solution is [Given: pk, and pKa2 of H2CO3 are 6.37 and 10.32,...
6. Consider the following reaction. LOH red phosphorous Br2 R (major product) Br On estimation of bromine in 1.00 g of R using Carius method, the amount of AgBr formed (in g) is [Given: Atomic mass...
Median Home Prices. The median price for an existing home in the United States peaked at $221,900 in 2006 (National Association of REALTORS®). The quartic function h(x) = 56.8328x4 - 1554.7494x3...
An educational researcher devised a wooden toy assembly project to test learning in 6-year-olds. The time in seconds to assemble the project was noted, and the toy was disassembled out of the childs...
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 00 k 3 k=1
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is...
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is...
Lakeland Inc. manufactured 2,500 units during the month of March. They incurred direct materials cost of $58,000 and overhead costs of $40,000. If their per-unit prime cost was $32.00 per unit, how...
Present Value Computations Using the present value tables, solve the following. ( Click here to access the PV and FV tables to use with this problem. ) Round your answers to two decimal places....
A company provided the following data: Sales $887,000 Variable costs $546,800 Fixed costs $310,000 Expected production and sales in units 36,000 What is the break-even point in sales dollars? Please...

Consider the function (a) Show that as (x, y) (0, 0) along any line y =

Question:

f(x, y) = xy + 2y x

Step by Step Answer:

a Along the line y mx the limit is If m0 this simplifies to x mx lim x0 x 2mx mx x0 x4 2m lim 0 l...View the full answer

Calculus

Students also viewed these Mathematics questions