Question

Check the continuity of function at (0, 0)
f(x,y)=\[x^{2}y-xy ^{2}/x ^{2}+y ^{3}if f(x,y)\neq(0,0) and if(x,y)=(0,0)\]

Answer 1

Eman you're going to want to change this into polar coordinates

Answer 2

using x=rcos(theta) and y =rsin(theta)

Answer 3

you there?

Answer 4

yess

Answer 5

understand ?

Answer 6

so for every x replace with rcos(theta) and with ever y=rsin(theta) you should find a common factor of r's and cancel out some) you should get = 0

Answer 7

so it's continuous at (0,0)

Answer 8

thnx

Answer 9

you should get at the end like 0/cos^2(theta)