Question

sal... ma puteti ajuta va rog

Answer 1

$\text{Dupa ce amplificam cu conjugata obtinem:}\\ \displaystyle\limit\lim_{x\to \infty} (\sqrt{4x^2-5x+2}-2\sqrt{x^2-2x}) =\\ =\displaystyle\limit\lim_{x\to \infty} \dfrac{4x^2-5x+2-4x^2+8x}{\sqrt{4x^2-5x+2}+2\sqrt{x^2-2x}}=\\ =\displaystyle\limit\lim_{x\to \infty} \dfrac{3x+2}{\sqrt{4x^2-5x+2}+2\sqrt{x^2-2x}}=\\ \displaystyle\limit\lim_{x\to \infty} \dfrac{x\cdot \left(3+\frac{2}{x}\right)}{x\left(\sqrt{4-\frac{5}{x}+\frac{2}{x^2}}+2\sqrt{1-\frac{2}{x}}\right)}=\dfrac{3}{2+2}=\boxed{\dfrac{3}{4}}$