Question and Answers Forum

AllQuestion and Answers: Page 1080

Question Number 108776 Answers: 1 Comments: 0

⋮^(bobhans) ∫ (dx/( (√(x(√x) −x^2 )))) = ?

$$\:\overset{{bobhans}} {\vdots} \\ $$$$\int\:\frac{{dx}}{\:\sqrt{{x}\sqrt{{x}}\:−{x}^{\mathrm{2}} }}\:=\:? \\ $$

Question Number 108769 Answers: 1 Comments: 0

((⋰BeMath⋱)/★) Given ((2x)/(2x+6)) = ((5y)/(5y+25)) = ((4z)/(4z+16)) and xy + yz + xz = 188 . Find the solution

$$\:\:\:\frac{\iddots\mathcal{B}{e}\mathcal{M}{ath}\ddots}{\bigstar} \\ $$$$\:\mathrm{G}{iven}\:\frac{\mathrm{2}{x}}{\mathrm{2}{x}+\mathrm{6}}\:=\:\frac{\mathrm{5}{y}}{\mathrm{5}{y}+\mathrm{25}}\:=\:\frac{\mathrm{4}{z}}{\mathrm{4}{z}+\mathrm{16}} \\ $$$${and}\:{xy}\:+\:{yz}\:+\:{xz}\:=\:\mathrm{188}\:.\:\mathrm{F}{ind}\:{the} \\ $$$${solution} \\ $$

Question Number 108766 Answers: 5 Comments: 0

((BeMath)/★) (1) find the equation of the tangent line to the graph of the equation sin^(−1) (x)+cos^(−1) (y)=(π/2) at given point (((√2)/2), ((√2)/2)) (2)If f(x)= lim_(t→x) ((sec t−sec x)/(t−x)) , find the value of f ′((π/4)) (3) lim_(x→1) ((tan^(−1) (x)−(π/4))/(x−1))

$$\:\:\:\frac{\mathcal{B}{e}\mathcal{M}{ath}}{\bigstar} \\ $$$$\left(\mathrm{1}\right)\:{find}\:{the}\:{equation}\:{of}\:{the}\:{tangent}\:{line}\:{to} \\ $$$${the}\:{graph}\:{of}\:{the}\:{equation}\:\mathrm{sin}^{−\mathrm{1}} \left({x}\right)+\mathrm{cos}^{−\mathrm{1}} \left({y}\right)=\frac{\pi}{\mathrm{2}} \\ $$$${at}\:{given}\:{point}\:\left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}},\:\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right) \\ $$$$\left(\mathrm{2}\right){If}\:{f}\left({x}\right)=\:\underset{{t}\rightarrow{x}} {\mathrm{lim}}\:\frac{\mathrm{sec}\:{t}−\mathrm{sec}\:{x}}{{t}−{x}}\:,\:{find}\:{the}\:{value}\:{of}\: \\ $$$${f}\:'\left(\frac{\pi}{\mathrm{4}}\right) \\ $$$$\left(\mathrm{3}\right)\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{tan}^{−\mathrm{1}} \left({x}\right)−\frac{\pi}{\mathrm{4}}}{{x}−\mathrm{1}} \\ $$

Question Number 108761 Answers: 2 Comments: 0

((⋮((Be)/(Math))⋮)/★) If ∫_(−1) ^( a) ((x+1)/((x+2)^4 )) = ((10)/(81)) , then the value of a−2 is ___

$$\:\:\:\frac{\vdots\frac{\mathcal{B}{e}}{\mathcal{M}{ath}}\vdots}{\bigstar} \\ $$$${If}\:\int_{−\mathrm{1}} ^{\:\:{a}} \:\frac{{x}+\mathrm{1}}{\left({x}+\mathrm{2}\right)^{\mathrm{4}} }\:=\:\frac{\mathrm{10}}{\mathrm{81}}\:,\:{then}\:{the}\:{value}\:{of} \\ $$$${a}−\mathrm{2}\:{is}\:\_\_\_ \\ $$

Question Number 108753 Answers: 2 Comments: 4

((⋮BeMath⋮)/△) (((√x) +1)/(x(√x) +x+(√x))) : (1/( (√x) −x^2 )) + x = ?

$$\:\:\frac{\vdots\mathcal{B}{e}\mathcal{M}{ath}\vdots}{\bigtriangleup} \\ $$$$\:\frac{\sqrt{{x}}\:+\mathrm{1}}{{x}\sqrt{{x}}\:+{x}+\sqrt{{x}}}\::\:\frac{\mathrm{1}}{\:\sqrt{{x}}\:−{x}^{\mathrm{2}} }\:+\:{x}\:=\:?\: \\ $$

Question Number 108750 Answers: 2 Comments: 0

calculste ∫_0 ^∞ ((ln(x))/(x^2 −x+1))dx

$$\mathrm{calculste}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$

Question Number 108749 Answers: 2 Comments: 0

calculste ∫_0 ^∞ ((ln(x))/((1+x)^4 )) dx

$$\mathrm{calculste}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{4}} }\:\mathrm{dx} \\ $$

Question Number 108748 Answers: 1 Comments: 0

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