Question

Lim 3x²-x+lnx/5lnx+x-4x²
x->∞
Rezolvare

Answer 1

$\lim\limits_{x\to\infty} \dfrac{3x^2-x+\ln x}{-4x^2+x-5\ln x} = \\ \\ = \lim\limits_{x\to\infty} \dfrac{x^2(3-\frac{1}{x}+\frac{\ln x}{x^2})}{x^2(-4+\frac{1}{x}-\frac{5\ln x}{x^2})} = \\ \\ = \dfrac{3-0+0}{-4+0-0} = \boxed{-\dfrac{3}{4}}\\ \\ \lim\limits_{x\to\infty} \dfrac{\ln x}{x^2} = \lim\limits_{x\to\infty} \dfrac{\frac{1}{x}}{2x} = \dfrac{1}{2x^2} = 0$