Question

Solução do limite seguinte:

Answer 1

Olá!

$\displaystyle \lim_{x\to\infty}\dfrac{10x^3+5x^2-2x+1}{mx^3+4x^2-3x+9}=$

$\displaystyle =\lim_{x\to\infty}\dfrac{x^3(10+\frac{5}{x}-\frac{2}{x^2}+\frac{1}{x^3})}{x^3(m+\frac{4}{x}-\frac{3}{x^2}+\frac{9}{x^3})}=$

$\displaystyle =\lim_{x\to\infty}\dfrac{(10+\frac{5}{x}-\frac{2}{x^2}+\frac{1}{x^3})}{(m+\frac{4}{x}-\frac{3}{x^2}+\frac{9}{x^3})}\;\overset{x\to\infty}{=}\;\dfrac{10}{m}$

$\therefore \dfrac{10}{m}=5\Rightarrow m=2.$


Bons estudos!