Question

Giúp ạ lim x->+ vô cùng (x-1)^2 / x(x^2 + 5)

Answer 1

\(\lim\limits_{x\rightarrow+\infty}\dfrac{\left(x-1\right)^2}{x\left(x^2+5\right)}=\lim\limits_{x\rightarrow+\infty}\dfrac{x^2-2x+1}{x\left(x^2+5\right)}\)

\(=\lim\limits_{x\rightarrow+\infty}\dfrac{1-\dfrac{2}{x}+\dfrac{1}{x^2}}{x\left(1+\dfrac{5}{x^2}\right)}=\lim\limits_{x\rightarrow+\infty}\dfrac{1}{x}\cdot\lim\limits_{x\rightarrow+\infty}\dfrac{1-\dfrac{2}{x}+\dfrac{1}{x^2}}{1+\dfrac{5}{x^2}}\)

\(=+\infty\) vì \(\left\{{}\begin{matrix}\lim\limits_{x\rightarrow+\infty}\dfrac{1}{x}=+\infty\\\lim\limits_{x\rightarrow+\infty}\dfrac{1-\dfrac{2}{x}+\dfrac{1}{x^2}}{1+\dfrac{5}{x^2}}=\dfrac{1}{1}=1>0\end{matrix}\right.\)