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lim-x-0-cos-2x-sin-x2-




Question Number 6668 by janzmir6996 last updated on 10/Jul/16
lim_(x→0) cos 2x/sin x2
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}cos}\:\mathrm{2}{x}/\mathrm{sin}\:{x}\mathrm{2} \\ $$
Commented by Rasheed Soomro last updated on 10/Jul/16
Do you mean    lim_(x→0)   cos 2x/sin x^2    ?
$${Do}\:{you}\:{mean}\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\mathrm{cos}\:\mathrm{2}{x}/\mathrm{sin}\:{x}^{\mathrm{2}} \:\:\:? \\ $$
Answered by FilupSmith last updated on 10/Jul/16
lim_(x→0)  ((cos 2x)/(sin x^2 )) = ((cos(0))/(sin(0^2 ))) = ∞
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{sin}\:{x}^{\mathrm{2}} }\:=\:\frac{\mathrm{cos}\left(\mathrm{0}\right)}{\mathrm{sin}\left(\mathrm{0}^{\mathrm{2}} \right)}\:=\:\infty \\ $$

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