# Evaluating limit in multivariable calculus problem

$$\lim_{(x,y)\to(0,0)}\frac{(2x+y)\sin(x+y)}{(x+y)\sin(2x+y)}$$

• @Kevin What have you tried so far? – SplitInfinity Feb 29 '16 at 21:49
• I have tried multiplying by the conjugate of x-y but I am very stuck – EconDude Feb 29 '16 at 21:51
• $\lim_{t\to 0}(\sin t) / t = 1$ is all you need – user147263 Feb 29 '16 at 21:53
• oh boy wow thank you totally forgot about that! – EconDude Feb 29 '16 at 21:53
• You can edit your answer to include what you tried, instead of mentioning it in a comment. In general, questions (and answers) are seen as primary on Stack Exchange sites, whereas comments are regarded as secondary. – J W Feb 29 '16 at 22:04

## 1 Answer

Take $x+y=z$ and $2x+y=w$, then $z$ and $w$ tend to zero as $x$ and $y$ tend to zero and use the above-mentioned limit $\lim_{t\to 0}(\sin t) / t = 1$.