Question

cho biết \(\lim\limits_{x\rightarrow-\infty}\dfrac{1-\sqrt{4x^2-x+5}}{a\left|x\right|+2}=\dfrac{2}{3}\). tính giá trị a?

Answer 1

\(=\lim\limits_{x\rightarrow-\infty}\dfrac{1-\sqrt{4x^2-x+5}}{-ax+2}=\lim\limits_{x\rightarrow-\infty}\dfrac{\dfrac{1}{x}+\sqrt{4-\dfrac{1}{x}+\dfrac{5}{x^2}}}{-a+\dfrac{2}{x}}=\dfrac{2}{-a}=\dfrac{2}{3}\)

\(\Rightarrow a=-3\)