Question

biết \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{3x^2+2}-\sqrt{2-2x}}{x}=\dfrac{a\sqrt{2}}{b}\). tìm a,b biết a/b tối giản

Answer 1

\(\lim\limits_{x\rightarrow0}\dfrac{3x^2+2-\left(2-2x\right)}{x\left(\sqrt{3x^2+2}+\sqrt{2-2x}\right)}=\lim\limits_{x\rightarrow0}\dfrac{x\left(3x+2\right)}{x\left(\sqrt{3x^2+2}+\sqrt{2-2x}\right)}\)

\(=\lim\limits_{x\rightarrow0}\dfrac{3x+2}{\sqrt{3x^2+2}+\sqrt{2-2x}}=\dfrac{2}{2\sqrt{2}}=\dfrac{\sqrt{2}}{2}\)

\(\Rightarrow\left\{{}\begin{matrix}a=1\\b=2\end{matrix}\right.\)