Giải thích các bước giải:
Ta có:
$\lim_{x\to-\infty}\dfrac{(x^3-x-2)^7}{(x^2-2x+16)^{10}}$
$=\lim_{x\to-\infty}\dfrac{(x^3(1-\dfrac1{x^2}-\dfrac2{x^3})^7}{(x^2(1-\dfrac2x+\dfrac{16}{x^2})^{10}}$
$=\lim_{x\to-\infty}\dfrac{x^{21}(1-\dfrac1{x^2}-\dfrac2{x^3})^7}{x^{20}(1-\dfrac2x+\dfrac{16}{x^2})^{10}}$
$=\lim_{x\to-\infty}\dfrac{x(1-\dfrac1{x^2}-\dfrac2{x^3})^7}{(1-\dfrac2x+\dfrac{16}{x^2})^{10}}$
$=\dfrac{-\infty\cdot (1-0-0)^7}{(1-0+0)^{10}}$
$=-\infty$
