Question

I = lim x -> +∞ (✓(9x ^ 2 - 2x + 3) - 3x ^ 2)

Answer 1

\(=\lim\limits_{x\rightarrow+\infty}\left(\sqrt{9x^2-2x+3}-3x^2\right)\)

\(=\lim\limits_{x\rightarrow+\infty}\dfrac{9x^2-2x+3-3x^4}{3x^2+\sqrt{9x^2-2x+3}}\)

\(=\lim\limits_{x\rightarrow+\infty}\dfrac{-3x^4+9x^2-2x+3}{3x^2+\sqrt{9x^2-2x+3}}\)

\(=\lim\limits_{x\rightarrow+\infty}x^2\dfrac{-3+\dfrac{9}{x^2}-\dfrac{2}{x^3}+\dfrac{3}{x^4}}{3+\sqrt{\dfrac{9}{x}-\dfrac{2}{x^2}+\dfrac{3}{x^2}}}=-\infty\)