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Question Number 186064 by TUN last updated on 31/Jan/23

$$\underset{x\to \mathrm{\infty }}{\lim }(cos2x-cos\sqrt{4x^2+10})$$$$$$

Commented by a.lgnaoui last updated on 31/Jan/23

$$2x=t$$$$\cos 2x-\cos \sqrt{4x^2+10}=\cos t-\cos t\sqrt{1+\frac{10}{t^2}}$$$$=\cos t(1-\sqrt{1+\frac{10}{t^2}})$$$$x\to \mathrm{\infty }t\to \mathrm{\infty }$$$$1-\sqrt{1+\frac{1}{t^2}}\to 0$$$$donc{\lim }_{\mathrm{x}\to \mathrm{\infty }}(\cos 2x-\cos \sqrt{4x^2+10})=\stackrel{}{0}$$

Answered by Frix last updated on 01/Feb/23

$$\sqrt{4x^2+10}\sim 2x\Rightarrow \mathrm{answer}\mathrm{is}0$$

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