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$\lim_{x \to 0} \frac{x + 2\sin x}{\sqrt{x^2 + 2\sin x + 1} - \sqrt{\sin^2 x - x + 1}}$ is:
(1) $6$
(2) $2$
(3) $3$
(4) $1$
Rationalising: $\lim_{x\to 0}\frac{(x+2\sin x)\left[\sqrt{x^2+2\sin x+1} + \sqrt{\sin^2 x - x + 1}\right]}{(x^2 - \sin^2 x) + (x + 2\sin x)} = \frac{3 \times 2}{3} = 2$.
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