Question: Graph and discuss the continuity of the function (a) Show that f (x, y) 0 as (x, y) (0, 0) along any path

Graph and discuss the continuity of the function sin xy f(х, у) — if ху %# 0 if ху — 0 ху

(a) Show that f (x, y) → 0 as (x, y) → (0, 0) along any path through (0, 0) of the form y = mx^a with 0 < a < 4.
(b) Despite part (a), show that f is discontinuous at (0, 0).
(c) Show that f is discontinuous on two entire curves.

sin xy f(, ) if %# 0 if 0

Step by Step Solution

★★★★★

3.33 Rating (174 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

fx y sinxy xy lim xy ab on R From the graph it appea... View full answer

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!

A cell phone company charges $0.12 for connecting a call plus $0.08 per minute or any part thereof (e.g., a phone call lasting 2 minutes and 5 seconds costs $0.12 + 3 $0.08). Sketch a graph of the...

A rental car company charges $20 for one day, allowing up to 200 miles. For each additional 100 miles, or any fraction thereof, the company charges $18. Sketch a graph of the cost for renting a car...

A cab company charges $2.50 for the first 1/4 mile and $0.20 for each additional 1/8 mile. Sketch a graph of the cost of a cab ride as a function of the number of miles driven. Discuss the continuity...

Example 12 Discuss the continuity of the function defined by x+2, if x 0 Solution Observe that the function is defined at all real numbers except at 0. Domain of definition of this...

Let (a) Show that f (x, y) 0 as (x, y) (0, 0) along any path through (0, 0) of the form y = mx a with 0

3:08 LIE 1 54.0 KB/S 13% K Practical 1 (part 1).pdf . . Practical 1 . 1) Define a function of as follows: f ( * ) = if * * 2 1 1 21 = 2 check whether the given function is continuous at the Point #2"...

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

UNIVERISTY HELPP IN HERE NOT for TUTOR: dont submit if you dont do full THEM OR BAD RATE And in full explanation show all your work Solve the following system of nonlinear equations:x^2 + y^2 = 9 x^2...

A 1200-W electric resistance heating element whose diameter is 0.5 cm is immersed in 40 kg of water initially at 20C. Assuming the water container is well-insulated, determine how long it will take...

A portion of a circular cylindrical shell forms a small vane which is welded to the vertical shaft AB. The vane and shaft rotate about the y axis with a constant angular velocity of 180 rpm...

Show the process of button - up parsing for parsing for a b c d $ Start S $ S A C C c A aBCd B Q B b B Q q Figure 1 : Parse Table

1. What challenges does Coach face relative to pricing its vast product line? pg98

Return to the analysis of my undying love for my wife expressed through weekly purchases of roses (as introduced in end-of-chapter exercise 6.4). A. Recall that initially roses cost $5 each and, with...

Suppose, as in end-of-chapter exercise 6.9, you have $400,000 to spend on square feet of housing and all other goods. Assume the same is true for me. A. Suppose again that you initially face a $100...

Every Thanksgiving, my wife and I debate about how we should prepare the turkey we will serve (and will then have left over). My wife likes preparing turkeys the conventional way roasted in the oven...

PROBLEMV A company has 1 0 , 0 0 0 shares of $ 1 0 par common stock outstanding. Present entries to record the following: ( a ) Purchased 1 , 0 0 0 shares of treasury stock at $ 1 3 . The treasury...

83 Analysts have evaluated the Sivar Silver Company and discovered that if sales are Leverage Analys $800,000 the following will exist: Degree of operating leverage (DOL) Degree of financial leverage...

Modern Artifacts can produce keepsakes that will be sold for $60 each. Nondepreciation fixed costs are $2,500 per year, and variable costs are $30 per unit. The initial investment of $4,000 will be...