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schmidt7100
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Homework Statement
Show that the function f(x,y)= xy/sqrt(x^2+y^2) is continuous at the origin using polar coordinates. f(x,y)=0 if (x,y)=(0,0)
Homework Equations
r=sqrt(x^2+y^2)
x=rcos(theta)
y=rsin(theta)
The Attempt at a Solution
So, converting this equation to polar coordinates, I get rsin(theta)cos(theta). However, after this I'm stumped as to how I prove that this is continuous at the origin.