I'm having trouble with this problem

f(x,y)= {(sin(x^2+y^2 )/((x^2+y^2 ) ) (x,y)=(0,0)

1 (x,y)≠(0,0)

The question says to show that f is continuous

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- Apr 6th 2010, 08:59 PMghow90Two-Variable Limit and Continuity
I'm having trouble with this problem

f(x,y)= {(sin(x^2+y^2 )/((x^2+y^2 ) ) (x,y)=(0,0)

1 (x,y)≠(0,0)

The question says to show that f is continuous - Apr 6th 2010, 09:10 PMProve It
- Apr 6th 2010, 09:11 PMghow90
- Apr 7th 2010, 03:02 AMHallsofIvy
Notice that Prove It changed to polar coordinates. That simplifies the problem greatly- since just r itself measures the distance to (0,0) regardless of . As long as the limit, as r goes to 0, does NOT depend on [tex]\theta[\math], that gives the correct limit.