Multivariable Limit Problem

I am having some problems with the following problems:

1. $\displaystyle \lim_{\theta\to 0}\frac{sin\theta}{\theta}

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Using l'Hôpital's rule I got that the limit equals.

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

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I am not really sure how to proceed here. I mean, I could approach along the y axis, then am I able to use l'Hôpital's rule?Also, if I approach along y = x afterward I believe I would get 2 for the limit, whereas along the y-axis would yield 1 provided I could use l'Hôpital's rule. In that case the limit would not exist.

3.$\displaystyle \lim_{(x,y)\to (0,0)}\frac{sin(xy)}{xy}

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On this one I don't really know what to do.