Polar Co-ordinates: f(x,y) = sin(x^2 + y^2) / (x^2 + y^2)

[petrol.veem]

How does one convert the following into polar co-ordinates and then take the limit as (x,y)-->(0,0)?

f(x,y) = [sin(x^2 + y^2)] / [x^2 + y^2]

 

[stapel]

What basic polar-coordinate identity do you have for x² + y²? :wink:

Eliz.

 

[galactus]

If you make the appropriate substitution for x^2+y^2, then you will have a well-known limit.

 

[petrol.veem]

ok, i see the how the polar co-ordinate one solves now.

the second part of the question asks to solve the limit using the epsilon-delta approach. I am having trouble getting started. any ideas?

 

[stapel]

How about using the "well-known limit" from Calc I, mentioned previously?

Eliz.