Đáp án:
$\lim\limits_{x\to 0}\dfrac{(1+x)^5 - (1+5x)}{x^5 + x^2} = 10$
Giải thích các bước giải:
$\quad \lim\limits_{x\to 0}\dfrac{(1+x)^5 - (1+5x)}{x^5 + x^2}$
$=\lim\limits_{x\to 0}\dfrac{(x^5 + 5x^4 + 10x^3 + 10x^2 + 5x +1) - 1 - 5x}{x^5 + x^2}$
$=\lim\limits_{x\to 0}\dfrac{x^2(x^3 + 5x^2 + 10x +10)}{x^2(x^3 +1)}$
$= \lim\limits_{x\to 0}\dfrac{x^3 + 5x^2 + 10x +10}{x^3 +1}$
$=\dfrac{0^3 + 5.0^2 + 10.0 + 10}{0^3 +1}$
$= 10$
