Need to prove this function is continuous f(x,y)=sin(xy)/sqrt(x^2 + y^2) [ analytically ]
Now |f(x,y)-f(a,b)|
<=|f(x,y)|+|f(a,b)|
<=|1/sqrt(x^2 + y^2)| + |1/sqrt(a^2 + b^2)|
<= 1/|x| + 1/|a|
= (|x|+|a|)/|a||x|
<=( x^2 + a^2)/|a||x| .
I am getting stuck at this position . Any ideas ? . Consider any neighborhood circular or square.
Now |f(x,y)-f(a,b)|
<=|f(x,y)|+|f(a,b)|
<=|1/sqrt(x^2 + y^2)| + |1/sqrt(a^2 + b^2)|
<= 1/|x| + 1/|a|
= (|x|+|a|)/|a||x|
<=( x^2 + a^2)/|a||x| .
I am getting stuck at this position . Any ideas ? . Consider any neighborhood circular or square.