Question

Lim при х➡️к бесконечности (1-x-x^3)/(x^3+3)

Answer 1

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Answer 2

$\lim _{x\to \infty \:}\left(\frac{1-x-x^3}{x^3+3}\right) = \lim _{x\to \infty \:}\left(\frac{\frac{1}{x^3}-\frac{1}{x^2}-1}{1+\frac{3}{x^3}}\right)= \\ \\ =\frac{\lim _{x\to \infty \:}\left(\frac{1}{x^3}-\frac{1}{x^2}-1\right)}{\lim _{x\to \infty \:}\left(1+\frac{3}{x^3}\right)} \\$

$\lim _{x\to \infty \:}\left(\frac{1}{x^3}-\frac{1}{x^2}-1\right) = \\ \\ = lim_{x\to \infty \:}\left(\frac{1}{x^3}\right)-\lim _{x\to \infty \:}\left(\frac{1}{x^2}\right)-\lim _{x\to \infty \:}\left(1\right) = 0-0-1=-1 \\ \\ \\ \lim _{x\to \infty \:}\left(1+\frac{3}{x^3}\right)=\lim _{x\to \infty \:}\left(1\right)+\lim _{x\to \infty \:}\left(\frac{3}{x^3}\right)=1+0=1 \\ \\ \frac{-1}{1} =-1 \\ OTBET \boxed{-1}$