Question

Tìm các giới hạn:

\(a.lim\left(-2x^{-3}+x+1\right)\)

\(b.\lim\limits_{x\rightarrow+\infty}\dfrac{2x^2+1}{3-x}\)

\(c.\lim\limits_{x\rightarrow0^+}\dfrac{x+1}{\sqrt{x}}\)

Answer 1

Câu a thiếu giới hạn tới đâu rồi em

\(\lim\limits_{x\rightarrow+\infty}=\lim\limits_{x\rightarrow+\infty}\dfrac{x\left(2x+\dfrac{1}{x}\right)}{x\left(\dfrac{3}{x}-1\right)}=\lim\limits_{x\rightarrow+\infty}\dfrac{2x+\dfrac{1}{x}}{\dfrac{3}{x}-1}=\dfrac{+\infty}{-1}=-\infty\)

\(\lim\limits_{x\rightarrow0^+}\dfrac{x+1}{\sqrt{x}}=\lim\limits_{x\rightarrow0^+}\dfrac{\sqrt{x}\left(\sqrt{x}+\dfrac{1}{\sqrt{x}}\right)}{\sqrt{x}}=\lim\limits_{x\rightarrow0^+}\left(\sqrt{x}+\dfrac{1}{\sqrt{x}}\right)=0+\infty=+\infty\)