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Question Number 89270 Answers: 0 Comments: 0

what is the maximum perimeter of a parallelogram ABCD which inscribed the ellipse (x^2 /4) + y^2 = 1 ?

$${what}\:{is}\:{the}\:{maximum}\: \\ $$$${perimeter}\:{of}\:{a}\:{parallelogram}\: \\ $$$${ABCD}\:{which}\:{inscribed}\:{the}\: \\ $$$${ellipse}\:\frac{{x}^{\mathrm{2}} }{\mathrm{4}}\:+\:{y}^{\mathrm{2}} \:=\:\mathrm{1}\:? \\ $$

Question Number 89268 Answers: 0 Comments: 0

Please help with this summation. Σ_(k = 0) ^n (− 1)^k ^n C_k y_(n − k) = ???

Question Number 89275 Answers: 1 Comments: 1

Question Number 89273 Answers: 1 Comments: 0

Evaluate ∫_0 ^1 (x^2 /(√(1+x^3 )))dx and given that I_(n ) =∫_0 ^1 x^n (1+x^3 )^(−(1/2)) dx show that (2n−1)I_n =2(√2)−2(n−1) for n≥3. Hence evaluate I_8 , I_7 and I_6

$${Evaluate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{2}} }{\sqrt{\mathrm{1}+{x}^{\mathrm{3}} }}{dx}\:{and}\:{given}\:{that}\:{I}_{{n}\:} =\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} \left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{−\frac{\mathrm{1}}{\mathrm{2}}} {dx} \\ $$$${show}\:{that}\:\left(\mathrm{2}{n}−\mathrm{1}\right){I}_{{n}} =\mathrm{2}\sqrt{\mathrm{2}}−\mathrm{2}\left({n}−\mathrm{1}\right)\:{for}\:{n}\geqslant\mathrm{3}. \\ $$$${Hence}\:{evaluate}\:{I}_{\mathrm{8}} ,\:{I}_{\mathrm{7}} \:{and}\:{I}_{\mathrm{6}} \\ $$

Question Number 89271 Answers: 0 Comments: 1

(3/4)×(8/9)×((15)/(16))×...×((2499)/(2500))

$$\frac{\mathrm{3}}{\mathrm{4}}×\frac{\mathrm{8}}{\mathrm{9}}×\frac{\mathrm{15}}{\mathrm{16}}×...×\frac{\mathrm{2499}}{\mathrm{2500}} \\ $$

Question Number 89311 Answers: 0 Comments: 0

Show that ∫_( 0) ^( 1) {∫_( 0) ^( 1) ((x−y)/((x+y)^2 ))dy}dx=∫_( 0) ^( 1) {∫_( 0) ^( 1) ((x−y)/((x+y)^2 ))dx}dy

$$\:\:{Show}\:{that} \\ $$$$\underset{\:\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\:\mathrm{1}} {\int}}\left\{\underset{\:\:\:\:\mathrm{0}} {\overset{\:\:\:\mathrm{1}} {\int}}\frac{{x}−{y}}{\left({x}+{y}\right)^{\mathrm{2}} }{dy}\right\}{dx}=\underset{\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\:\mathrm{1}} {\int}}\left\{\underset{\:\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\mathrm{1}} {\int}}\frac{{x}−{y}}{\left({x}+{y}\right)^{\mathrm{2}} }{dx}\right\}{dy} \\ $$$$ \\ $$

Question Number 89259 Answers: 0 Comments: 2

hello any good books to learn calculas and series?

$${hello}\: \\ $$$${any}\:{good}\:{books}\:{to}\:{learn}\:{calculas}\:{and} \\ $$$${series}? \\ $$

Question Number 89255 Answers: 0 Comments: 3

1⟩Σ_(k=2) ^∞ (1/(k^n k!)) 2⟩∫_0 ^∞ (xe^(1−x) −⌊x⌋e^(1−⌊x⌋) )dx

$$\mathrm{1}\rangle\underset{{k}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{k}^{{n}} {k}!} \\ $$$$\mathrm{2}\rangle\int_{\mathrm{0}} ^{\infty} \left({xe}^{\mathrm{1}−{x}} −\lfloor{x}\rfloor{e}^{\mathrm{1}−\lfloor{x}\rfloor} \right){dx} \\ $$

Question Number 89244 Answers: 0 Comments: 1

Question Number 89243 Answers: 3 Comments: 0

solve the following diffirntial equation 1)(2x+y)dx+(x+y)dy=0 2)(3x−y)dx−(x−y)dy=0 3) (cos(x)+y)dx + (2y+x)dy=0

$${solve}\:{the}\:{following}\:{diffirntial}\:{equation} \\ $$$$\left.\mathrm{1}\right)\left(\mathrm{2}{x}+{y}\right){dx}+\left({x}+{y}\right){dy}=\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\left(\mathrm{3}{x}−{y}\right){dx}−\left({x}−{y}\right){dy}=\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\:\left({cos}\left({x}\right)+{y}\right){dx}\:+\:\left(\mathrm{2}{y}+{x}\right){dy}=\mathrm{0} \\ $$

Question Number 89237 Answers: 0 Comments: 1

∫_2 ^1 (x+1)((√(x+3)))

$$\int_{\mathrm{2}} ^{\mathrm{1}} \left(\mathrm{x}+\mathrm{1}\right)\left(\sqrt{\left.\mathrm{x}+\mathrm{3}\right)}\right. \\ $$

Question Number 89236 Answers: 1 Comments: 0

z(z^2 +3x)+3y=0 show that (∂^2 z/∂x^2 )+(∂^2 z/∂y^2 )=((2z(x−1))/((z^2 +x)^3 ))

$$\mathrm{z}\left(\mathrm{z}^{\mathrm{2}} +\mathrm{3x}\right)+\mathrm{3y}=\mathrm{0} \\ $$$$\mathrm{show}\:\mathrm{that} \\ $$$$\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{x}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{y}^{\mathrm{2}} }=\frac{\mathrm{2z}\left(\mathrm{x}−\mathrm{1}\right)}{\left(\mathrm{z}^{\mathrm{2}} +\mathrm{x}\right)^{\mathrm{3}} } \\ $$

Question Number 89240 Answers: 0 Comments: 0

If I_n =∫_0 ^π e^x sin^n xdx, show that (n^2 +1)I_n =n(n−1)I_(n−2)

$${If}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\pi} {e}^{{x}} {sin}^{{n}} {xdx},\:{show}\:{that}\: \\ $$$$\left({n}^{\mathrm{2}} +\mathrm{1}\right){I}_{{n}} ={n}\left({n}−\mathrm{1}\right){I}_{{n}−\mathrm{2}} \\ $$

Question Number 89238 Answers: 1 Comments: 1

∫_7 ^(12) x^2 (√(x−3))

$$\int_{\mathrm{7}} ^{\mathrm{12}} \mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}−\mathrm{3}} \\ $$

Question Number 89226 Answers: 0 Comments: 1

∫(((x^3 +2)/x^3 ))(√(x−(1/x^2 )))

$$\int\left(\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{2}}{\mathrm{x}^{\mathrm{3}} }\right)\sqrt{\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }} \\ $$

Question Number 89239 Answers: 0 Comments: 5

A new update has been released to fix issues with android 10. If you have android 10 phone please download latest update.

$$\mathrm{A}\:\mathrm{new}\:\mathrm{update}\:\mathrm{has}\:\mathrm{been}\:\mathrm{released}\:\mathrm{to} \\ $$$$\mathrm{fix}\:\mathrm{issues}\:\mathrm{with}\:\mathrm{android}\:\mathrm{10}.\:\mathrm{If}\:\mathrm{you} \\ $$$$\mathrm{have}\:\mathrm{android}\:\mathrm{10}\:\mathrm{phone}\:\mathrm{please}\:\mathrm{download} \\ $$$$\mathrm{latest}\:\mathrm{update}. \\ $$

Question Number 89213 Answers: 1 Comments: 0

∫((√(tan x + 1))/(cos^2 x))

$$\int\frac{\sqrt{\mathrm{tan}\:\mathrm{x}\:+\:\mathrm{1}}}{\mathrm{cos}^{\mathrm{2}} \mathrm{x}} \\ $$

Question Number 89228 Answers: 0 Comments: 1

∫_4 ^5 x^2 (√(x−4))

$$\underset{\mathrm{4}} {\overset{\mathrm{5}} {\int}}\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}−\mathrm{4}} \\ $$

Question Number 89205 Answers: 1 Comments: 1

2 (dy/dx) = (y/x) + ((y/x))^2

$$\mathrm{2}\:\frac{{dy}}{{dx}}\:=\:\frac{{y}}{{x}}\:+\:\left(\frac{{y}}{{x}}\right)^{\mathrm{2}} \\ $$

Question Number 89202 Answers: 0 Comments: 4

sin ((π/7))sin (((2π)/7))sin (((3π)/7)) =?

$$\mathrm{sin}\:\left(\frac{\pi}{\mathrm{7}}\right)\mathrm{sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:=? \\ $$

Question Number 89200 Answers: 0 Comments: 0

Question Number 89194 Answers: 1 Comments: 2

Question Number 89193 Answers: 0 Comments: 3

cos x−sin x =(1/2) cos x sin x = (3/8) , π < x < 2π cos x + sin x =?

$$\mathrm{cos}\:{x}−\mathrm{sin}\:{x}\:=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{cos}\:{x}\:\mathrm{sin}\:{x}\:=\:\frac{\mathrm{3}}{\mathrm{8}}\:,\:\pi\:<\:{x}\:<\:\mathrm{2}\pi \\ $$$$\mathrm{cos}\:{x}\:+\:\mathrm{sin}\:{x}\:=? \\ $$

Question Number 89192 Answers: 2 Comments: 2

Question Number 89188 Answers: 2 Comments: 0

f(x) + f(x−1) = x^2 , x ∈ R f(19) = 94 f(94) = ... ?

$${f}\left({x}\right)\:+\:{f}\left({x}−\mathrm{1}\right)\:\:=\:\:{x}^{\mathrm{2}} \:\:\:,\:\:\:{x}\:\in\:\mathbb{R} \\ $$$${f}\left(\mathrm{19}\right)\:\:=\:\:\mathrm{94} \\ $$$${f}\left(\mathrm{94}\right)\:\:=\:\:...\:\:? \\ $$

Question Number 89187 Answers: 0 Comments: 2

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