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Question Number 97073 Answers: 3 Comments: 4

Find (dy/dx) of 2^x + y^2 = 2xy , x, y ∈ C

$${Find}\:\:\frac{{dy}}{{dx}}\:\:{of}\:\:\:\:\mathrm{2}^{{x}} \:+\:{y}^{\mathrm{2}} \:=\:\mathrm{2}{xy}\:\:\:\:,\:\:{x},\:{y}\:\in\:\mathbb{C} \\ $$

Question Number 97068 Answers: 1 Comments: 1

Question Number 97067 Answers: 2 Comments: 1

if p is the natural number then what is the degree of x^(6p+1) +3x^(4p−3) +4x^(8p−10) +8 polynomial?

$$\mathrm{if}\:\mathrm{p}\:\mathrm{is}\:\mathrm{the}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{degree}\:\mathrm{of} \\ $$$$\mathrm{x}^{\mathrm{6p}+\mathrm{1}} +\mathrm{3x}^{\mathrm{4p}−\mathrm{3}} +\mathrm{4x}^{\mathrm{8p}−\mathrm{10}} +\mathrm{8}\:\:\mathrm{polynomial}? \\ $$

Question Number 97064 Answers: 0 Comments: 1

find the value of (an) in this utility (3xy^2 )^3

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{an}\right)\:\mathrm{in}\:\mathrm{this}\:\mathrm{utility}\:\:\left(\mathrm{3xy}^{\mathrm{2}} \right)^{\mathrm{3}} \\ $$

Question Number 97059 Answers: 0 Comments: 1

Question Number 97057 Answers: 2 Comments: 0

∫_0 ^1 (dx/(√(−ln(x)))) ? [ by Gamma function ]

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\sqrt{−\mathrm{ln}\left({x}\right)}}\:?\:\left[\:{by}\:{G}\mathrm{amma}\:\mathrm{function}\:\right] \\ $$

Question Number 97065 Answers: 0 Comments: 2

Question Number 97055 Answers: 0 Comments: 0

Question Number 97051 Answers: 2 Comments: 2

what is the perimeter of a regular dodecagon (12 sides) whose area is 24+12(√3) ?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{a}\:\mathrm{regular}\: \\ $$$$\mathrm{dodecagon}\:\left(\mathrm{12}\:\mathrm{sides}\right)\:\mathrm{whose}\: \\ $$$$\mathrm{area}\:\mathrm{is}\:\mathrm{24}+\mathrm{12}\sqrt{\mathrm{3}}\:?\: \\ $$

Question Number 97045 Answers: 0 Comments: 4

a committee consisting of 5 men & 4 women is to be chosen from 8 men & 4 women. If one man & one woman are husband & wife , how many ways can the committee be chosen if only one of the husband & wife must be chosen ?

$$\mathrm{a}\:\mathrm{committee}\:\mathrm{consisting}\:\mathrm{of} \\ $$$$\mathrm{5}\:\mathrm{men}\:\&\:\mathrm{4}\:\mathrm{women}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\: \\ $$$$\mathrm{chosen}\:\mathrm{from}\:\mathrm{8}\:\mathrm{men}\:\&\:\mathrm{4}\:\mathrm{women}. \\ $$$$\mathrm{If}\:\mathrm{one}\:\mathrm{man}\:\&\:\mathrm{one}\:\mathrm{woman}\:\mathrm{are}\:\mathrm{husband}\: \\ $$$$\&\:\mathrm{wife}\:,\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\: \\ $$$$\mathrm{the}\:\mathrm{committee}\:\mathrm{be}\:\mathrm{chosen}\:\mathrm{if} \\ $$$$\mathrm{only}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{husband}\:\&\:\mathrm{wife} \\ $$$$\mathrm{must}\:\mathrm{be}\:\mathrm{chosen}\:? \\ $$

Question Number 97041 Answers: 2 Comments: 0

∫ sin^8 (x) cos^8 (x) dx = ?

$$\int\:\mathrm{sin}\:^{\mathrm{8}} \left({x}\right)\:\mathrm{cos}\:^{\mathrm{8}} \left({x}\right)\:{dx}\:=\:? \\ $$

Question Number 97033 Answers: 1 Comments: 0

Question Number 97031 Answers: 0 Comments: 0

Question Number 97019 Answers: 0 Comments: 1

Question Number 97011 Answers: 0 Comments: 0

Let Γ be the gamma function Prove that Σ_(n=0) ^∞ Res(Γ;−n)= e

$${Let}\:\:\Gamma\:{be}\:{the}\:{gamma}\:{function}\:\: \\ $$$$\:{Prove}\:{that}\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{Res}\left(\Gamma;−{n}\right)=\:{e} \\ $$

Question Number 97007 Answers: 0 Comments: 16

Question Number 97005 Answers: 1 Comments: 2

Question Number 97001 Answers: 1 Comments: 2

solve (1+x^2 ) (dy/dx) = xy−xy^2

$$\mathrm{solve}\:\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{xy}−\mathrm{xy}^{\mathrm{2}} \\ $$

Question Number 96990 Answers: 1 Comments: 0

∫_0 ^1 ((√x))^(√x) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\sqrt{\mathrm{x}}\right)^{\sqrt{\mathrm{x}}} \mathrm{dx} \\ $$

Question Number 96979 Answers: 1 Comments: 0

∫_0 ^π arctan(3^(cos(x)) )dx

$$\int_{\mathrm{0}} ^{\pi} {arctan}\left(\mathrm{3}^{{cos}\left({x}\right)} \right){dx} \\ $$

Question Number 96977 Answers: 1 Comments: 0

lim_(x→5) ((x − 5)/(2 + cot^2 (2/(x −5))))

$$\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\:\frac{{x}\:−\:\mathrm{5}}{\mathrm{2}\:+\:\mathrm{cot}^{\mathrm{2}} \frac{\mathrm{2}}{{x}\:−\mathrm{5}}} \\ $$

Question Number 96962 Answers: 1 Comments: 0

find ∫_0 ^1 (dx/((√(x+1))+(√(2x^2 +1))))

$$\mathrm{find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{dx}}{\sqrt{\mathrm{x}+\mathrm{1}}+\sqrt{\mathrm{2x}^{\mathrm{2}} +\mathrm{1}}} \\ $$

Question Number 96959 Answers: 1 Comments: 0

find ∫ arctan(x−(1/x))dx

$$\mathrm{find}\:\int\:\mathrm{arctan}\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}\right)\mathrm{dx} \\ $$

Question Number 96958 Answers: 0 Comments: 0

let g(x) =ln(tanx) developp f at fourier serie

$$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)\:=\mathrm{ln}\left(\mathrm{tanx}\right) \\ $$$$\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 96957 Answers: 2 Comments: 0

find ∫ x^3 (√(2−x−x^2 ))dx

$$\mathrm{find}\:\int\:\mathrm{x}^{\mathrm{3}} \sqrt{\mathrm{2}−\mathrm{x}−\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 96956 Answers: 2 Comments: 0

calculate ∫_(−∞) ^∞ ((x^2 −3)/((x^2 −x+1)^3 ))dx

$$\mathrm{calculate}\:\int_{−\infty} ^{\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{3}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} }\mathrm{dx} \\ $$

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