Question: Let Is continuous at the origin? Why? f(x, y) = sin (x - y) |x] + [y] 0, |x + y = 0 (x,

Letf(x, y) = sin (x - y) |x] + [y] 0, |x


Is ƒ continuous at the origin? Why?

f(x, y) = sin (x - y) |x] + [y] 0, |x + y = 0 (x, y) = (0,0).

Step by Step Solution

★★★★★

3.34 Rating (148 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

No is not continuous at the origin To see why consider appr... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Q:

Graph the function to see whether it appears to have a continuous extension to the origin. If it does, use Trace and Zoom to find a good candidate for the extended functions value at x = 0. If the...

Q:

Graph the function to see whether it appears to have a continuous extension to the origin. If it does, use Trace and Zoom to find a good candidate for the extended functions value at x = 0. If the...

Q:

Graph the function to see whether it appears to have a continuous extension to the origin. If it does, use Trace and Zoom to find a good candidate for the extended functions value at x = 0. If the...

Q:

Recall that lim sin ( ) does not exist, lim x sin ( ) = 0, and lim x2 sin () = 0. x-+0 x-+0 Thus if we define the functions f and g by f (x) = x sin (for x # 0, f(0 = 0, g(x) = x2 sin ( for x * 0,...

Q:

Use the coordinate axis provided to sketch the graph of a function with the given characteristics. (1) Domain is x * -3. (2) Continuous on (-0o, -3) . (3) Continuous on (-3,0). (4) Continuous on...

Q:

1 ) Calculate the average value of the function f (x) = x sin (5x) over the interval 0 x /4. Give its value to the nearest 0.001 2) Calculate the average value of the function f (x) = x (x^2 + 2)^2...

Q:

806 Chapter Fifteen OPTIMIZATION: LOCAL AND GLOBAL EXTREMA If f is not continuous or the region R is not closed and bounded, there is no guarantee that f achieves a global maximum or global minimum...

Q:

please use this format filename 1 .. 10 name file 2 1 .. 10 1. Find the derivative of f if f (I) = 2-50. Preview will appear here.. Enter math expression here 2. Differentiate the function F(y) =...

Q:

Question 4 (15 p) Assume that national income, Y, is exogenously set at one fixed level (full employment) in both the short-run and in the long-run, and that the exchange rate is floating. Assume...

Q:

HHelp me to solve the questions as attached below. 3. Consider an economy with A consumers and B rms. Each consumer is endowed with one unit of time and one piece of capital. A representative...

Q:

The education minister of a country ensures that 80% of the university students have a monthly income for their maintenance, superior at $570,000; you want to refute the minister with a confidence...

Q:

You have a part-time work/study job at the library that pays $10 per hour, 3 hours per day on Saturdays and Sundays. Some friends want you to join them on a weekend ski trip leaving Friday night and...

Q:

Fix The Fortran Code Below: program resampking implicit none integer, parameter :: ns = 1 0 0 0 0 real, dimension ( 4 ) :: WC 1 = [ 0 . 8 , 1 . 2 , 1 . 6 , 5 . 2 ] real, dimension ( 5 ) :: WCex = [ 3...

Q:

12.32 The following passage is from the paper Gender Differences in Food Selections of Students at a Historically Black College and University (College Student Journal [2009]: 800806): Also...

Q:

Consider the parametric equations (a) Use a graphing utility to graph the curve represented by the parametric equations.(b) Use a graphing utility to find the points of horizontal tangency to the...

Q:

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The curve given by x = h + a cos and y = k + b sin has two horizontal...

Q:

The rectangular coordinates of a point are given. Plot the point and find two sets of polar coordinates for the point for 0 =

Q:

Corporation strategy and business (or competitive) strategy. Company is Under Armour's Strategy in 2014 1) What have been the key elements of the companys corporate strategy up until the time of the...

Q:

During 2021, a company selis 480 units of inventory for $92 each. The company has the following inventory purchase transactions for 2021: Calculate cost of goods sold and ending inventory for 2021...

Q:

Topic 5: Accounting for foreign currency transactions MyBeauty Ltd is an Australian company which specialises in manufacturing and distributing health and beauty products to both local and...