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lim-x-0-1-cos-x-cos-2x-cos-3x-1-3-cos-4x-1-4-x-2-




Question Number 156250 by cortano last updated on 09/Oct/21
    lim_(x→0)  ((1−cos x (√(cos 2x)) ((cos 3x))^(1/3)  ((cos 4x))^(1/4) )/x^2 ) =?
$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{x}\:\sqrt{\mathrm{cos}\:\mathrm{2x}}\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{3x}}\:\sqrt[{\mathrm{4}}]{\mathrm{cos}\:\mathrm{4x}}}{\mathrm{x}^{\mathrm{2}} }\:=? \\ $$
Commented by john_santu last updated on 09/Oct/21
limit=((4×5)/4)=5
$${limit}=\frac{\mathrm{4}×\mathrm{5}}{\mathrm{4}}=\mathrm{5} \\ $$

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