calculus - Verification of the limit of $(x-sin(x))/(tan(x)-x)$ as $xto 0$

I would appreciate if someone could verify to me my answers.

$$\lim_{x\rightarrow0}\frac{x-\sin(x)}{\tan(x)-x}$$ I used L'Hopital's rule twice and got answer $1/2$.
$$\lim_{x\rightarrow0^+}\frac{1}{\sin(4x)}-\frac{1}{4x}$$ also I used L'Hopital's rule twice and got $0$.
$$\lim_{x\rightarrow2^-}(x^2-4)\ln(2-x)$$ I used L'Hopital's rule once and got $0$.

Thanks.

Answer

Since the answer to the first problem has been given by GTX OC, let us focus on the second problem.

$$(x^2-4) \log(2-x) = (x-2)(x+2)\log(2-x)=-(x+2)(2-x)\log(2-x)$$
I suppose you know that $x \log(x)$ goes to 0 when $x$ goes to zero. Then, ... Are you able to continue with this ?