Question

tìm giới hạn \(\lim\limits_{x\rightarrow+\infty}\left(x+1-\sqrt{x^2-x+2}\right)\)

Answer 1

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

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