Question Number 195075 by tri26112004 last updated on 23/Jul/23
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{sin}^{\mathrm{2}} {x}−{cos}^{\mathrm{3}} {x}}{{x}} \\ $$
Answered by MM42 last updated on 23/Jul/23
$$\exists\:{m}>\mathrm{0}\:;\:\forall\:{x}\in\mathbb{R}\:\Rightarrow\:\mid{sin}^{\mathrm{2}} {x}−{cos}^{\mathrm{3}} {x}\mid\leqslant{m} \\ $$$$\&\:\:{lim}_{{x}\rightarrow\infty} \:\frac{\mathrm{1}}{{x}}=\mathrm{0}\Rightarrow{lim}_{{x}\rightarrow\infty} \:\frac{{sin}^{\mathrm{2}} {x}−{cos}^{\mathrm{3}} {x}}{{x}}\:=\mathrm{0} \\ $$