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Question Number 142708 Answers: 1 Comments: 0

I=∫_0 ^( α) (√(c^2 −sin^2 θ))dθ tan α=(a^2 /b^2 ) , a^2 >b^2 , c^2 >1 Perimeter of ellipse =4∫_0 ^( π/2) (√(a^2 −(a^2 −b^2 )sin^2 θ)) dθ (is that right sir?)

$$\:{I}=\int_{\mathrm{0}} ^{\:\:\alpha} \sqrt{{c}^{\mathrm{2}} −\mathrm{sin}\:^{\mathrm{2}} \theta}{d}\theta \\ $$$$\:\mathrm{tan}\:\alpha=\frac{{a}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:\:,\:{a}^{\mathrm{2}} >{b}^{\mathrm{2}} \:\:,\:{c}^{\mathrm{2}} >\mathrm{1} \\ $$$${Perimeter}\:{of}\:{ellipse} \\ $$$$=\mathrm{4}\int_{\mathrm{0}} ^{\:\:\pi/\mathrm{2}} \sqrt{{a}^{\mathrm{2}} −\left({a}^{\mathrm{2}} −{b}^{\mathrm{2}} \right)\mathrm{sin}\:^{\mathrm{2}} \theta}\:{d}\theta \\ $$$$\left({is}\:{that}\:{right}\:{sir}?\right) \\ $$

Question Number 142698 Answers: 1 Comments: 0

Prove that ∀n∈N^∗ Π_(k=1) ^(n−1) sin(((kπ)/(2n))) = Π_(k=1) ^(n−1) cos(((kπ)/(2n)))

$$\mathrm{Prove}\:\mathrm{that}\:\forall\mathrm{n}\in\mathbb{N}^{\ast} \\ $$$$\:\:\:\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\prod}}\mathrm{sin}\left(\frac{\mathrm{k}\pi}{\mathrm{2n}}\right)\:=\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\prod}}\mathrm{cos}\left(\frac{\mathrm{k}\pi}{\mathrm{2n}}\right) \\ $$

Question Number 142691 Answers: 1 Comments: 1

The number of distributions of 52 cards divided equally to 4 persons so as each gets 4 cards of same suit taken away from 3suits(4×3=12)℘ remaining card from remaining 4 th suit is

$${The}\:{number}\:{of}\:{distributions}\:{of}\:\mathrm{52} \\ $$$${cards}\:{divided}\:{equally}\:{to}\:\mathrm{4}\:{persons}\:{so} \\ $$$${as}\:{each}\:{gets}\:\mathrm{4}\:{cards}\:{of}\:{same}\:{suit} \\ $$$${taken}\:{away}\:{from}\:\mathrm{3}{suits}\left(\mathrm{4}×\mathrm{3}=\mathrm{12}\right)\wp \\ $$$${remaining}\:{card}\:{from}\:{remaining} \\ $$$$\mathrm{4}\:{th}\:{suit}\:{is} \\ $$

Question Number 142690 Answers: 1 Comments: 0

∫_(0 ) ^1 ((log(x)log((x/(1−x))))/( (√(x/(1−x)))))dx Any help

$$\int_{\mathrm{0}\:} ^{\mathrm{1}} \frac{\boldsymbol{{log}}\left(\boldsymbol{{x}}\right)\boldsymbol{{log}}\left(\frac{\boldsymbol{{x}}}{\mathrm{1}−\boldsymbol{{x}}}\right)}{\:\sqrt{\frac{\boldsymbol{{x}}}{\mathrm{1}−\boldsymbol{{x}}}}}\boldsymbol{{dx}} \\ $$$$\boldsymbol{\mathrm{Any}}\:\boldsymbol{\mathrm{help}}\: \\ $$$$ \\ $$

Question Number 142689 Answers: 1 Comments: 0

Question Number 142687 Answers: 1 Comments: 0

∫ (dx/( (√(1−sin x)) (√(1+cos x)))) =?

$$\:\:\:\:\:\:\int\:\frac{{dx}}{\:\sqrt{\mathrm{1}−\mathrm{sin}\:{x}}\:\sqrt{\mathrm{1}+\mathrm{cos}\:{x}}}\:=? \\ $$

Question Number 142681 Answers: 0 Comments: 2

prove that :: 𝛗:=∫_0 ^( ∞) ((ln(1+cos(x)))/(1+e^( x) ))dx=0 ................

$$ \\ $$$$\:\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left(\mathrm{1}+{cos}\left({x}\right)\right)}{\mathrm{1}+{e}^{\:{x}} }{dx}=\mathrm{0} \\ $$$$\:\:\:\:\:................ \\ $$$$ \\ $$

Question Number 142679 Answers: 0 Comments: 5

how to get exert value of a lambert w function question without wolfram alpha

$${how}\:{to}\:{get}\:{exert}\:{value}\:{of}\:{a}\:{lambert}\:{w}\:{function}\:{question}\:{without}\:{wolfram}\:{alpha} \\ $$

Question Number 142668 Answers: 3 Comments: 2

lim_(n→∞) (((n+6)/n))^(6/n) = ?

$$\underset{{n}\rightarrow\infty} {{lim}}\left(\frac{{n}+\mathrm{6}}{{n}}\right)^{\frac{\mathrm{6}}{{n}}} =\:? \\ $$

Question Number 142667 Answers: 1 Comments: 0

Question Number 142655 Answers: 2 Comments: 0

evaluate..... Σ_(n=1) ^∞ (((n.cos(nπ))/(Γ (2n+2))))=? ..... .......

$$\:\:{evaluate}..... \\ $$$$\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{{n}.{cos}\left({n}\pi\right)}{\Gamma\:\left(\mathrm{2}{n}+\mathrm{2}\right)}\right)=?\:..... \\ $$$$\:\:\:....... \\ $$

Question Number 142656 Answers: 2 Comments: 0

∫_(−π) ^π ((xsin x)/(1+x^2 ))dx=?

$$\int_{−\pi} ^{\pi} \frac{\mathrm{xsin}\:\mathrm{x}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}=? \\ $$

Question Number 142653 Answers: 2 Comments: 0

x^3 .e^x =216

$${x}^{\mathrm{3}} .{e}^{{x}} =\mathrm{216} \\ $$

Question Number 142647 Answers: 2 Comments: 0

(1/(2018))−(2/(2018))+(3/(2018))−(4/(2018))+...−((2016)/(2018))+((2017)/(2018))=?

$$\:\frac{\mathrm{1}}{\mathrm{2018}}−\frac{\mathrm{2}}{\mathrm{2018}}+\frac{\mathrm{3}}{\mathrm{2018}}−\frac{\mathrm{4}}{\mathrm{2018}}+...−\frac{\mathrm{2016}}{\mathrm{2018}}+\frac{\mathrm{2017}}{\mathrm{2018}}=? \\ $$

Question Number 142646 Answers: 1 Comments: 0

Prove that (1+(1/2^3 ))(1+(1/3^3 ))(1+(1/4^3 )) … < 3

$${Prove}\:\:{that} \\ $$$$\:\:\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{3}} }\right)\:\ldots\:<\:\mathrm{3} \\ $$

Question Number 142643 Answers: 1 Comments: 0

∫_0 ^(π/2) ((cos^2 t)/(sint))dt

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{cos}^{\mathrm{2}} {t}}{{sint}}{dt} \\ $$

Question Number 142639 Answers: 2 Comments: 2

Question Number 142674 Answers: 1 Comments: 0

If f(x)=((x−3)/(x+1)) and h(x)=f(f(f(f(..2022 times(f(x)))))) then h(1) =?

$${If}\:{f}\left({x}\right)=\frac{{x}−\mathrm{3}}{{x}+\mathrm{1}}\:{and}\:{h}\left({x}\right)={f}\left({f}\left({f}\left({f}\left(..\mathrm{2022}\:{times}\left({f}\left({x}\right)\right)\right)\right)\right)\right) \\ $$$${then}\:\:\:{h}\left(\mathrm{1}\right)\:=? \\ $$

Question Number 142630 Answers: 0 Comments: 1

Given f(x)=(1/(1+2^x )) find the value of f((1/(2018)))×f((3/(2018)))×f(((2015)/(2018)))×f(((2017)/(2018)))=?

$$\:{Given}\:{f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}^{{x}} } \\ $$$${find}\:{the}\:{value}\:{of} \\ $$$${f}\left(\frac{\mathrm{1}}{\mathrm{2018}}\right)×{f}\left(\frac{\mathrm{3}}{\mathrm{2018}}\right)×{f}\left(\frac{\mathrm{2015}}{\mathrm{2018}}\right)×{f}\left(\frac{\mathrm{2017}}{\mathrm{2018}}\right)=? \\ $$

Question Number 142629 Answers: 1 Comments: 0

Σ_(n=1) ^∞ (−1)^n ∙((2n−1)/((2n)!))∙((π/2))^(2n) =Σ_(n=1) ^∞ ((2n−1)/((2n)!))∙(−((π/2))^2 )^n =(2xD−1)∣_(x=π/2) Σ_(n=1) ^∞ (((−x^2 )^n )/((2n)!)) =(2xD−1)∣_(x=π/2) [Σ_(n=0) ^∞ (((−x^2 )^n )/((2n)!))−1] =(2xD−1)∣_(x=π/2) (cos x−1) =(−2xsin x−cos x+1)∣_(x=π/2) =1−π where is wrong?

$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{n}} \centerdot\frac{\mathrm{2n}−\mathrm{1}}{\left(\mathrm{2n}\right)!}\centerdot\left(\frac{\pi}{\mathrm{2}}\right)^{\mathrm{2n}} \\ $$$$=\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{2n}−\mathrm{1}}{\left(\mathrm{2n}\right)!}\centerdot\left(−\left(\frac{\pi}{\mathrm{2}}\right)^{\mathrm{2}} \right)^{\mathrm{n}} \\ $$$$=\left(\mathrm{2xD}−\mathrm{1}\right)\mid_{\mathrm{x}=\pi/\mathrm{2}} \underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} }{\left(\mathrm{2n}\right)!} \\ $$$$=\left(\mathrm{2xD}−\mathrm{1}\right)\mid_{\mathrm{x}=\pi/\mathrm{2}} \left[\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} }{\left(\mathrm{2n}\right)!}−\mathrm{1}\right] \\ $$$$=\left(\mathrm{2xD}−\mathrm{1}\right)\mid_{\mathrm{x}=\pi/\mathrm{2}} \left(\mathrm{cos}\:\mathrm{x}−\mathrm{1}\right) \\ $$$$=\left(−\mathrm{2xsin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}+\mathrm{1}\right)\mid_{\mathrm{x}=\pi/\mathrm{2}} \\ $$$$=\mathrm{1}−\pi \\ $$$$\mathrm{where}\:\mathrm{is}\:\mathrm{wrong}? \\ $$

Question Number 142627 Answers: 0 Comments: 0

Question Number 142624 Answers: 0 Comments: 0

fine the equation and the corresponding sketch of graph of the imageof the straight line joining (−1,−1) and (2,1) under the transformation equation w=(2+i)z

$${fine}\:{the}\:{equation}\:{and}\:{the}\:{corresponding} \\ $$$${sketch}\:{of}\:{graph}\:{of}\:{the}\:{imageof}\:{the} \\ $$$${straight}\:{line}\:{joining}\:\left(−\mathrm{1},−\mathrm{1}\right)\:{and} \\ $$$$\left(\mathrm{2},\mathrm{1}\right)\:{under}\:{the}\:{transformation}\:{equation} \\ $$$${w}=\left(\mathrm{2}+{i}\right){z} \\ $$

Question Number 142623 Answers: 2 Comments: 0

find the zero of z^3 +729=0 z∈C

$${find}\:{the}\:{zero}\:{of}\:{z}^{\mathrm{3}} +\mathrm{729}=\mathrm{0} \\ $$$${z}\in\mathbb{C} \\ $$

Question Number 142622 Answers: 1 Comments: 0

find z for which f(z)=(z/(sinz)) is undefined where z∈C

$${find}\:{z}\:{for}\:{which}\:{f}\left({z}\right)=\frac{{z}}{{sinz}}\:{is}\:{undefined} \\ $$$${where}\:{z}\in\mathbb{C} \\ $$

Question Number 142607 Answers: 1 Comments: 0

Question Number 142604 Answers: 1 Comments: 0

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