<s>[INST] Find the limit $\lim_{\theta\to 0} \frac{\sin \theta}{3\theta + \tan \theta}$ Given problem
$$\lim_{\theta\to 0} \frac{\sin \theta}{3\theta + \tan \theta}$$
I got to 
$$\lim_{\theta \to 0} \frac{\sin \theta \cos \theta}{3\theta \cos \theta + \sin \theta}$$
Now I'm lost. Any advice on how to be more efficient?
 [/INST] Since both $\sin\theta$ and $3\theta + \tan \theta$ tend to $0$ as $\theta\to0$, we use L'Hôptial's rule
$$\lim_{\theta\to 0} \frac{\sin \theta}{3\theta + \tan \theta}=\lim_{\theta\to 0} \frac{\cos \theta}{3 + \sec^2 \theta} = \frac{1}{3+1} = \frac14.$$
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