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**Lambin** PROBLEM:

$\displaystyle \lim_{x\to\0}\frac{sin(x)}{tan(x)+x}$

ATTEMPT:

I'm stumped on this one for two reasons. (1) I don't see any trigonometric identities that would be convenient to help evaluate the limit, and (2) when I transformed the expression in terms of sine and cosine (to make apparent the properties of limits), it doesn't seem to work either.

Here's what I've done:

$\displaystyle \lim_{x\to\0}\frac{sin(x)}{tan(x)+x}=\lim_{x\to\0} \frac{sin(x)cos(x)}{sin(x)+xcos(x)}$

If I attempted to use properties of limits to evaluate the expression in parts, but it's not very useful unless I could do something about the denominator:

$\displaystyle \lim_{x\to\0}(\frac{sin(x)}{x})(\frac{xcos(x)}{sin (x)+xcos(x)})$

Any ideas?