# Limit of a function of more than one variable

## Main Question or Discussion Point

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

tiny-tim
Homework Helper
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!

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
$$$|(x+y)sin\frac{1}{x}sin\frac{1}{y}|\leq |x+y|\rightarrow 0 (as x,y\rightarrow 0)$$$