I am unable to find these limits:
1) $ \lim_{x \to 1} \frac{3(1 - x^2) - 2(1 - x^3)}{(1 - x^3)(1 - x^2)} $
2) $ \lim_{x \to 0} \frac{\sqrt{1 - 2x - x^2} - (x + 1)}{x} $
3) $ \lim_{x \to 0} \frac{\sqrt{x + 2} + \sqrt{x + 6} - \sqrt{6} - \sqrt{2}}{x} $
4) $ \lim_{x \to 0} \frac{1 - \sqrt[3]{1 - x}}{1 + \sqrt[3]{3x - 1}} $
My interest is not in the answers, but in the algebraic manipulations i can use to eliminate the indeterminations of the type $0/0$.
My english skills are not so good, i'm sorry for this.