15). lim x→0 1-√2x+1 x

Решение:

$$\lim_{x \to 0} \frac{1 - \sqrt{2x+1}}{x} = \lim_{x \to 0} \frac{(1 - \sqrt{2x+1})(1 + \sqrt{2x+1})}{x(1 + \sqrt{2x+1})} = \lim_{x \to 0} \frac{1 - (2x+1)}{x(1 + \sqrt{2x+1})} =$$

$$= \lim_{x \to 0} \frac{-2x}{x(1 + \sqrt{2x+1})} = \lim_{x \to 0} \frac{-2}{1 + \sqrt{2x+1}} = \frac{-2}{1 + \sqrt{1}} = \frac{-2}{2} = -1$$

Ответ: $$-1$$