(a) We have the function{xyx²+y²if (x, y) # (0,0),f(x, y) :if (x, y) = (0,0),(a) Findlim(x,y)→(0,0)f (x, y), if it exists, or show that the limit does not exist.(b) Calculate fæ(0,0) and fy(0,0) if they exist, otherwise explain why they don't exist.(c) Are fæ and fy continuous at (0,0)? Explain why.

We have to find the following given conditions according to the given condition

Answered: We have the function if (x, y) # (0,0),…

We have the function if (x, y) # (0,0), xy x²+y² f (x, y) if (x, y) = (0,0), (а) Find lim (x,y)→(0,0) f (x, y), if it exists, or show that the limit does not e (o o)

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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Question

(a)

We have the function
{
xy
x²+y²
if (x, y) # (0,0),
f(x, y) :
if (x, y) = (0,0),
(a) Find
lim
(x,y)→(0,0)
f (x, y), if it exists, or show that the limit does not exist.
(b) Calculate fæ(0,0) and fy(0,0) if they exist, otherwise explain why they don't exist.
(c) Are fæ and fy continuous at (0,0)? Explain why.

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