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Question Number 100037 by bobhans last updated on 24/Jun/20

lim_(x→∞)  x(√x) sin (2x) ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{x}\sqrt{\mathrm{x}}\:\mathrm{sin}\:\left(\mathrm{2x}\right)\:? \\ $$

Commented by bramlex last updated on 24/Jun/20

lim_(x→∞)  x(√x) = ∞ ∧ −1≤ sin 2x ≤ 1  lim_(x→∞) x(√x) sin 2x = ∞

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}\sqrt{{x}}\:=\:\infty\:\wedge\:−\mathrm{1}\leqslant\:\mathrm{sin}\:\mathrm{2}{x}\:\leqslant\:\mathrm{1} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}{x}\sqrt{{x}}\:\mathrm{sin}\:\mathrm{2}{x}\:=\:\infty\: \\ $$

Commented by Dwaipayan Shikari last updated on 24/Jun/20

∞

$$\infty \\ $$

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