Converting Sin to Absolute Value for Multi-Variable Limits

[brendan]

Homework Statement

Find the limit for x = 0 y= 0 for sin(x^2+y^2)/x^2+y^2

Homework Equations

I'm trying to use the squeeze method using the inequality |ab| <= 1/2(a^2+b^2)

The Attempt at a Solution

Is there a way I can convert sin(x^2+y^2) into absolute value |ab|

so I can get |ab| <= (1/2(x^2+y^2))/x^2+y^2


or should I use a different inequality?

 

[Mark44]

I don't think the approach you're attempting will do you any good. How about converting to polar coordinates? Then you're looking at the limit as r approaches zero.

 

[brendan]

Hi,

should I find the limit r -> 0 of sin(R^2)/R^2

= 1

regards

 

[Mark44]

That's what it looks like to me.

 

[brendan]

Thanks a lot!