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Question Number 168429 Answers: 2 Comments: 0

calculate: P=∫_1 ^e^(π/2) ((cos(lnx))/x)dx

$${calculate}: \\ $$$${P}=\int_{\mathrm{1}} ^{{e}^{\frac{\pi}{\mathrm{2}}} } \frac{{cos}\left({lnx}\right)}{{x}}{dx} \\ $$

Question Number 168446 Answers: 1 Comments: 0

Question Number 168428 Answers: 1 Comments: 0

solve f(x)= x +(√(x^( 2) −3x +2)) R _f =? R_( f) : rang of f

$$ \\ $$$$\:\:\:\:\:{solve} \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\:{x}\:+\sqrt{{x}^{\:\mathrm{2}} −\mathrm{3}{x}\:+\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:{R}\:_{{f}} \:=?\:\:\:\:\:\:\:{R}_{\:{f}} :\:{rang}\:{of}\:\:\:\:{f} \\ $$

Question Number 168427 Answers: 2 Comments: 2

Question Number 168421 Answers: 0 Comments: 0

Calculate the compound interest on the sum of #400 000 for 2years at the rate of 10% . Mastermind

$${Calculate}\:{the}\:{compound}\:{interest}\: \\ $$$${on}\:{the}\:{sum}\:{of}\:#\mathrm{400}\:\mathrm{000}\: \\ $$$${for}\:\mathrm{2}{years}\:{at}\:{the}\:{rate}\:{of} \\ $$$$\mathrm{10\%}\:. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168411 Answers: 0 Comments: 0

Question Number 168424 Answers: 0 Comments: 0

f(4)=5 f(5)=7 g(5)=3 g(7)=4 f(g(5))=?

$${f}\left(\mathrm{4}\right)=\mathrm{5}\:\:\:\:\:\:\:\:\:{f}\left(\mathrm{5}\right)=\mathrm{7} \\ $$$${g}\left(\mathrm{5}\right)=\mathrm{3}\:\:\:\:\:\:\:\:\:{g}\left(\mathrm{7}\right)=\mathrm{4} \\ $$$${f}\left({g}\left(\mathrm{5}\right)\right)=? \\ $$

Question Number 168405 Answers: 1 Comments: 2

Question Number 168402 Answers: 0 Comments: 1

2x^3 +9x^2 +13x+6=0 Solve the x, (Use Cubic Formula!) x_1 =? x_2 =? x_3 =?

$$\mathrm{2}{x}^{\mathrm{3}} +\mathrm{9}{x}^{\mathrm{2}} +\mathrm{13}{x}+\mathrm{6}=\mathrm{0} \\ $$$${Solve}\:{the}\:{x},\:\left({Use}\:{Cubic}\:{Formula}!\right) \\ $$$${x}_{\mathrm{1}} =? \\ $$$${x}_{\mathrm{2}} =? \\ $$$${x}_{\mathrm{3}} =? \\ $$

Question Number 168400 Answers: 0 Comments: 1

Question Number 168399 Answers: 1 Comments: 0

solve z^(1/4) −i=0 Mastermind

$${solve} \\ $$$${z}^{\frac{\mathrm{1}}{\mathrm{4}}} −{i}=\mathrm{0} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168391 Answers: 0 Comments: 1

((3(√3))/(3(√3)))=1 or 3×(√3)÷3×(√3) =3 ???

$$\:\:\:\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{3}\sqrt{\mathrm{3}}}=\mathrm{1}\:\:\:\:{or}\:\:\mathrm{3}×\sqrt{\mathrm{3}}\boldsymbol{\div}\mathrm{3}×\sqrt{\mathrm{3}}\:=\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:??? \\ $$

Question Number 168388 Answers: 1 Comments: 0

Question Number 168383 Answers: 2 Comments: 1

Question Number 168379 Answers: 0 Comments: 0

Question Number 168380 Answers: 0 Comments: 0

Question Number 168375 Answers: 0 Comments: 2

Question Number 168368 Answers: 1 Comments: 0

Question Number 168367 Answers: 1 Comments: 0

91x^2 +84y^2 −24xy+406x−392y+799=0 find the eccentricity,focus,length of major & minor axis,directrix & length of eccentric perpendicular

$$\mathrm{91}{x}^{\mathrm{2}} +\mathrm{84}{y}^{\mathrm{2}} −\mathrm{24}{xy}+\mathrm{406}{x}−\mathrm{392}{y}+\mathrm{799}=\mathrm{0} \\ $$$${find}\:{the}\:{eccentricity},{focus},{length}\:{of}\:{major}\:\&\:{minor}\:{axis},{directrix}\:\&\:{length}\:{of}\:{eccentric}\:{perpendicular} \\ $$$$ \\ $$

Question Number 168366 Answers: 1 Comments: 0

Question Number 168361 Answers: 1 Comments: 0

Question Number 168355 Answers: 1 Comments: 0

let U_n =∫_0 ^1 (x^n )(√(1−x^(2n+1) )))dx 1) find a equivalent of U_n (n∼∞) 2) study the comvergence of Σ U_n

$$\left.{let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \left({x}^{{n}} \right)\sqrt{\mathrm{1}−{x}^{\mathrm{2}{n}+\mathrm{1}} }\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{equivalent}\:{of}\:{U}_{{n}} \left({n}\sim\infty\right) \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{comvergence}\:{of}\:\Sigma\:{U}_{{n}} \\ $$

Question Number 168348 Answers: 2 Comments: 0

Question Number 168347 Answers: 1 Comments: 4

Question Number 168341 Answers: 1 Comments: 0

∫(1+x^2 )^3 dx=?

$$\int\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} {dx}=? \\ $$

Question Number 168339 Answers: 0 Comments: 0

A point in rectangular coordinates (x,y,z) can be represented in spherical coordinates (r,θ,ϕ) by: x = r sin θ sin ϕ, y = sin θ sin ϕ, z = sin ϕ, 0 ≤ θ ≤ 2π , 0 ≤ ϕ ≤ π (a) Calculate the Jacobian of the transformation ((∂(x,y,z))/(∂(r,θ,ϕ))) (b) Calculate the volume of the region delimited by the sphere: S = {x,y,z ∈R^3 , x^2 +y^2 +z^2 ≤ R^2 , R>0}

$$\mathrm{A}\:\mathrm{point}\:\mathrm{in}\:\mathrm{rectangular}\:\mathrm{coordinates}\: \\ $$$$\left({x},{y},{z}\right)\:\mathrm{can}\:\mathrm{be}\:\mathrm{represented}\:\mathrm{in}\:\mathrm{spherical} \\ $$$$\mathrm{coordinates}\:\left({r},\theta,\varphi\right)\:\mathrm{by}: \\ $$$$\:{x}\:=\:{r}\:\mathrm{sin}\:\theta\:\mathrm{sin}\:\varphi,\:{y}\:=\:\mathrm{sin}\:\theta\:\mathrm{sin}\:\varphi,\: \\ $$$${z}\:=\:\mathrm{sin}\:\varphi,\:\mathrm{0}\:\leqslant\:\theta\:\leqslant\:\mathrm{2}\pi\:,\:\mathrm{0}\:\leqslant\:\varphi\:\leqslant\:\pi \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{Jacobian}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{transformation}\:\frac{\partial\left({x},{y},{z}\right)}{\partial\left({r},\theta,\varphi\right)} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region} \\ $$$$\mathrm{delimited}\:\mathrm{by}\:\mathrm{the}\:\mathrm{sphere}: \\ $$$$\:\:{S}\:=\:\left\{{x},{y},{z}\:\in\mathbb{R}^{\mathrm{3}} \:,\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:\leqslant\:{R}^{\mathrm{2}} ,\:{R}>\mathrm{0}\right\} \\ $$

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