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Question Number 98823 by john santu last updated on 16/Jun/20

Commented by bramlex last updated on 16/Jun/20

$$L^{\prime }Hopital$$$$\underset{x\to 0}{\lim }\frac{\sin x+x\cos x}{3x^2}=\underset{x\to 0}{\lim }\frac{\cos x+\cos x-x\sin x}{6x}$$$$\underset{x\to 0}{\lim }\frac{2\cos x-x\sin x}{6x}=\mathrm{\infty }?$$

Commented by bemath last updated on 16/Jun/20

$$\underset{x\to 0}{\lim }\frac{x(x-\frac{1}{3}{x}^3+o\left(x^3\right))}{x^3}=$$$$\underset{x\to 0}{\lim }\frac{x-\frac{1}{3}{x}^3+o\left(x^3\right)}{x^2}=\mathrm{\infty }$$

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