Question

lim x -> 0 (x ^ 3 - x ^ 2 + 2x)/(x ^ 2 + x)

Answer 1

Ответ:

$\boldsymbol{\boxed{ \lim_{x \to 0} \frac{x^{3} - x^{2} + 2x}{x^{2} +x} = 2}}$

Пошаговое объяснение:

$\displaystyle \lim_{x \to 0} \frac{x^{3} - x^{2} + 2x}{x^{2} +x} = \lim_{x \to 0} \frac{x(x^{2} - x + 2)}{x(x +1)} = \lim_{x \to 0} \frac{(x^{2} - x + 2)}{(x +1)} = \frac{(0^{2} - 0 + 2)}{(0 +1)} =$

$= \dfrac{2}{1}=2$.