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Question Number 195075 by tri26112004 last updated on 23/Jul/23

$$\underset{x\to \mathrm{\infty }}{\lim }\frac{{sin}^{2}x-{cos}^{3}x}{x}$$

Answered by MM42 last updated on 23/Jul/23

$$\mathrm{\exists }m>0;\mathrm{\forall }x\in \mathbb{R}\Rightarrow \mid {sin}^{2}x-{cos}^{3}x\mid ⩽m$$$$\mathrm{\&}{lim}_{x\to \mathrm{\infty }}\frac{1}{x}=0\Rightarrow {lim}_{x\to \mathrm{\infty }}\frac{{sin}^{2}x-{cos}^{3}x}{x}=0$$

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