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Question Number 108757 Answers: 1 Comments: 0

((⋮BeMath⋮)/(▷♥⊲)) lim_(x→0) ((1−(√(cos xcos 2xcos 3xcos 4x...cos nx)))/x^2 ) =?

$$\:\:\frac{\vdots\mathcal{B}{e}\mathcal{M}{ath}\vdots}{\triangleright\heartsuit\triangleleft} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt{\mathrm{cos}\:{x}\mathrm{cos}\:\mathrm{2}{x}\mathrm{cos}\:\mathrm{3}{x}\mathrm{cos}\:\mathrm{4}{x}...\mathrm{cos}\:{nx}}}{{x}^{\mathrm{2}} }\:=? \\ $$

Question Number 108741 Answers: 2 Comments: 0

Solve x^3 −[x]=3 (x∈R)

$${Solve}\:{x}^{\mathrm{3}} −\left[{x}\right]=\mathrm{3} \\ $$$$\left({x}\in{R}\right) \\ $$

Question Number 108738 Answers: 0 Comments: 0

please: ^∗ prove^∗ :::: 1.^(important) lim_(z→1) (ζ (z) −(1/(z−1)) )= γ (euler constant) 2. ^(important) ∫_0 ^( ∞) (cos(x)−(1/(1+x^2 )))(dx/x) =− γ .....M.N.....

$$\:\:\:\:\:\:\:\:{please}:\:\:\:\:\:^{\ast} \mathrm{prove}^{\ast} :::: \\ $$$$\:\:\:\:\:\mathrm{1}.^{\mathrm{important}} \:\:\:\:\mathrm{lim}_{\mathrm{z}\rightarrow\mathrm{1}} \left(\zeta\:\left(\mathrm{z}\right)\:−\frac{\mathrm{1}}{\mathrm{z}−\mathrm{1}}\:\right)=\:\gamma\:\:\:\left(\mathrm{euler}\:\mathrm{constant}\right) \\ $$$$\:\:\:\:\mathrm{2}.\:\overset{\mathrm{important}} {\:}\:\:\int_{\mathrm{0}} ^{\:\infty} \left(\mathrm{cos}\left(\mathrm{x}\right)−\frac{\mathrm{1}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right)\frac{\mathrm{dx}}{\mathrm{x}}\:=−\:\gamma \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....\mathscr{M}.\mathscr{N}..... \\ $$$$\: \\ $$

Question Number 108728 Answers: 1 Comments: 0

Question Number 108727 Answers: 1 Comments: 0

Question Number 108725 Answers: 1 Comments: 0

The ratio of the profit, cost of materials and labour in the production of an article is 5:7:13 respectively. If the cost of materials is $ 840 more than that of labour, find the total cost of producing the article.

$$\mathrm{The}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{profit},\:\mathrm{cost}\:\mathrm{of}\:\mathrm{materials} \\ $$$$\mathrm{and}\:\mathrm{labour}\:\mathrm{in}\:\mathrm{the}\:\mathrm{production}\:\mathrm{of}\:\mathrm{an}\:\mathrm{article} \\ $$$$\mathrm{is}\:\mathrm{5}:\mathrm{7}:\mathrm{13}\:\mathrm{respectively}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{cost}\:\mathrm{of}\:\mathrm{materials} \\ $$$$\mathrm{is}\:\$\:\mathrm{840}\:\mathrm{more}\:\mathrm{than}\:\mathrm{that}\:\mathrm{of}\:\mathrm{labour},\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{total}\:\mathrm{cost}\:\mathrm{of}\:\mathrm{producing}\:\mathrm{the}\:\mathrm{article}. \\ $$

Question Number 108723 Answers: 2 Comments: 1