Question

qual o limite de [(2x^2-3x-5) / raiz quadrada (x^4+1)] quando x infinito

Answer 1

$\displaystyle\lim_{x\to\infty}\dfrac{2x^2-3x-5}{\sqrt{x^4+1}}\\\\\displaystyle\lim_{x\to\infty}\dfrac{x^2\left(2-\cancel{\dfrac{3}{x}}-\cancel{\dfrac{5}{x^2}}\right)}{\sqrt{x^4\left(1+\cancel{\dfrac{1}{x^4}}\right)}}\\\\\displaystyle\lim_{x\to\infty}\dfrac{x^2(2)}{\sqrt{x^4(1)}}\\\\\displaystyle\lim_{x\to\infty}\dfrac{2x^2}{x^2}=2\\\\\\\\\boxed{\boxed{\displaystyle\lim_{x\to\infty}\dfrac{2x^2-3x-5}{\sqrt{x^4+1}}=2}}$