I need help finding the the following limit:
lim
I tried to simplify to:
\lim_{x\rightarrow 0} \frac{\sin x \cos x}{x\cos x+\sin x}
but I don't know where to go from there. I think, at some point, you have to use the fact that \lim_{x\rightarrow 0} \frac{\sin x}{x} = 1. Any help would be appreciated.
Thanks!
Answer
\frac{\sin x}{x + \tan x} = \frac{1}{\frac{x}{\sin x}+\frac{\tan x}{\sin x}} \to 1/2
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