Q:

Multivariable limit - how to solve

I'm homelearning multivariable calculus and I am currently trying to solve the following limit:
$$\lim_{x\rightarrow 0, y\rightarrow 0}(x+y) \sin\frac{1}{x} \sin\frac{1}{y}$$
How should I solve it? I tried setting $(x,y)$ to $(0,0),$ but it's undefined and I don't know what else to try.
Thanks!

A:

Let $u$ and $v$ be any expressions having a value, then 
$$  -1 \leq \sin(u) \leq 1  $$
and 
$$  -1 \leq \sin(v) \leq 1  $$
so 
$$  -1 \leq \sin(u) \sin(v) \leq 1  \text{.}  $$
Consequently, 
$$  -1(x+y) \leq (x+y)\sin(1/x)\sin(1/y) \leq (x+y)  \text{.}  $$
Now apply the squeeze theorem.

