Question

a) lim \(\dfrac{2x-\sqrt{3x^2+2}}{5x+\sqrt{x^2+2}}\)

x-> +∞

b) lim \(\sqrt{\dfrac{x^2+1}{2x^4+x^2-3}}\)

x-> ∞

Answer 1

b/ \(=\lim\limits_{x\rightarrow+\infty}\sqrt{\dfrac{\dfrac{x^2}{x^4}+\dfrac{1}{x^4}}{\dfrac{2x^4}{x^4}+\dfrac{x^2}{x^4}-\dfrac{3}{x^4}}}=0\)

Answer 2

a/ \(=\lim\limits_{x\rightarrow+\infty}\dfrac{\dfrac{2x}{x}-\sqrt{\dfrac{3x^2}{x^2}+\dfrac{2}{x^2}}}{\dfrac{5x}{x}+\sqrt{\dfrac{x^2}{x^2}+\dfrac{2}{x^2}}}=\dfrac{2-\sqrt{3}}{5+1}=\dfrac{2-\sqrt{3}}{6}\)

b/ x tien toi duong vo cung hay am vo cung ban?