Limit of a function of more than one variable

[mathe]

Prove that
\lim_{x \to\0 ,y\rightarrow 0}(x+y)sin\frac{1}{x}sin\frac{1}{y}=0

 

[tiny-tim]

welcome to pf!

hi mathe! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[mathe]

hi mathe! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

Here's what I've tried
\[|(x+y)sin\frac{1}{x}sin\frac{1}{y}|\leq |x+y|\rightarrow 0 (as x,y\rightarrow 0)\]
but it seems to me so simple and too obvious...so I'm not sure about the solution

 

[tiny-tim]

hi mathe!

(you forgot to type "tex"! )

Here's what I've tried
\[|(x+y)sin\frac{1}{x}sin\frac{1}{y}|\leq |x+y|\rightarrow 0 (as x,y\rightarrow 0)\]
but it seems to me so simple and too obvious...so I'm not sure about the solution

looks fine to me