Finding the limit with three variables Here is the original problem: 
$$\lim_{(x,y,z)\to (0,0,0)}{(\cos x-1)\sin(2y)(e^{3z}-1)\over x^2yz}$$
I was thinking about splitting up the limit like this:
$$\lim_{(x,y,z)\to (0,0,0)}{(\cos x-1)\over x^2}\cdot\lim_{(x,y,z)\to (0,0,0)}{\sin(2y)\over y}\cdot\lim_{(x,y,z)\to (0,0,0)}{e^{3z}-1\over z}$$
And then break it down some more:$$\lim_{x\to 0}{(\cos x-1)\over x^2}\cdot\lim_{y\to 0}{\sin(2y)\over y}\cdot\lim_{z\to 0}{e^{3z}-1\over z}$$
And then I want to use L'Hospital's rule. If someone could let me know if I'm heading in the right direction or not, that would be great. Thanks!

If all the limits in sight exist, you're fine. 
