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

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    $\begingroup$ @Kevin What have you tried so far? $\endgroup$ – SplitInfinity Feb 29 '16 at 21:49
  • $\begingroup$ I have tried multiplying by the conjugate of x-y but I am very stuck $\endgroup$ – EconDude Feb 29 '16 at 21:51
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    $\begingroup$ $\lim_{t\to 0}(\sin t) / t = 1$ is all you need $\endgroup$ – user147263 Feb 29 '16 at 21:53
  • $\begingroup$ oh boy wow thank you totally forgot about that! $\endgroup$ – EconDude Feb 29 '16 at 21:53
  • $\begingroup$ 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. $\endgroup$ – J W Feb 29 '16 at 22:04
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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 $\lim_{t\to 0}(\sin t) / t = 1$.

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