multivariable limit problem I have a confusion regarding this problem.
Problem: $\displaystyle f(x,y)=\frac{\sin^2|x+2y|}{x^2+y^2}$ is continuous for all  $(x,y)\neq (0,0)$. True or false?
I think that the limit does not exist so the function is not continuous.
How to prove that limit does not exist?
Any help will be appreciated. Thanks in advance

Try approaching the limit by the line $y=k\cdot x$.
Applying the standard limit $$\lim_{t\rightarrow 0} \frac{\sin(t)}{t}$$
You can prove that the limit depends on the constant K, hence does not exist
