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Question Number 100088 Answers: 1 Comments: 1

calculate ∫ ((cosx)/(cos(3x)))dx

$$\mathrm{calculate}\:\int\:\frac{\mathrm{cosx}}{\mathrm{cos}\left(\mathrm{3x}\right)}\mathrm{dx} \\ $$

Question Number 100087 Answers: 1 Comments: 1

use beta function to calculate ∫_0 ^π sin^3 x(2+cosx)^6 dx

$$\mathrm{use}\:\mathrm{beta}\:\mathrm{function}\:\mathrm{to}\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\mathrm{sin}^{\mathrm{3}} \mathrm{x}\left(\mathrm{2}+\mathrm{cosx}\right)^{\mathrm{6}} \:\mathrm{dx} \\ $$

Question Number 100074 Answers: 1 Comments: 0

Question Number 100068 Answers: 2 Comments: 0

hello all i have some questions? 1)what is the riemann hypothesis? 2)how did they determine the distance to the sun? 3)how did we measure the speed of light?

$${hello}\:{all}\:{i}\:{have}\:{some}\:{questions}? \\ $$$$ \\ $$$$\left.\mathrm{1}\right){what}\:{is}\:{the}\:{riemann}\:{hypothesis}? \\ $$$$ \\ $$$$\left.\mathrm{2}\right){how}\:{did}\:{they}\:{determine}\:{the}\:{distance} \\ $$$${to}\:{the}\:{sun}? \\ $$$$ \\ $$$$\left.\mathrm{3}\right){how}\:{did}\:{we}\:{measure}\:{the}\:{speed}\:{of}\:{light}? \\ $$$$ \\ $$

Question Number 100065 Answers: 8 Comments: 0

Question Number 100054 Answers: 1 Comments: 0

I_(n,m) =∫_0 ^1 ∫_0 ^1 (((ln(x))^n (ln(y))^m )/(1−xy))dx dy

$${I}_{{n},{m}} =\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left({ln}\left({x}\right)\right)^{{n}} \left({ln}\left({y}\right)\right)^{{m}} }{\mathrm{1}−{xy}}{dx}\:{dy} \\ $$

Question Number 100053 Answers: 0 Comments: 0

Question Number 100048 Answers: 1 Comments: 0

Question Number 100047 Answers: 2 Comments: 0

∫_0 ^1 e^(−x^2 ) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{dx} \\ $$

Question Number 100042 Answers: 1 Comments: 0

Question Number 100040 Answers: 0 Comments: 2

Question Number 100037 Answers: 0 Comments: 2

lim_(x→∞) x(√x) sin (2x) ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{x}\sqrt{\mathrm{x}}\:\mathrm{sin}\:\left(\mathrm{2x}\right)\:? \\ $$

Question Number 100032 Answers: 1 Comments: 1

Given f((x/(x+1))) = x^2 . find minimum value of function h(x)=f(x)−(3/(x−1))

$$\mathrm{Given}\:\mathrm{f}\left(\frac{\mathrm{x}}{\mathrm{x}+\mathrm{1}}\right)\:=\:\mathrm{x}^{\mathrm{2}} \:.\:\mathrm{find}\:\mathrm{minimum}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{function}\:\mathrm{h}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}\right)−\frac{\mathrm{3}}{\mathrm{x}−\mathrm{1}} \\ $$

Question Number 100036 Answers: 1 Comments: 0

f(x)= (((√(1+sin 2x))−(√(1−2sin x)))/x) g(x) = 2x+ (√(2x)) . find lim_(x→0) g(f(x))

$$\mathrm{f}\left(\mathrm{x}\right)=\:\frac{\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{2x}}−\sqrt{\mathrm{1}−\mathrm{2sin}\:\mathrm{x}}}{\mathrm{x}} \\ $$$$\mathrm{g}\left(\mathrm{x}\right)\:=\:\mathrm{2x}+\:\sqrt{\mathrm{2x}}\:.\:\mathrm{find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{g}\left(\mathrm{f}\left(\mathrm{x}\right)\right) \\ $$

Question Number 100027 Answers: 1 Comments: 2

lim_(x→0) xsin ((1/x)) ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{xsin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:?\: \\ $$

Question Number 100026 Answers: 1 Comments: 0

∫_0 ^(π/2) e^(−sec^2 θ) dθ

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{e}^{−\mathrm{sec}^{\mathrm{2}} \theta} \mathrm{d}\theta \\ $$

Question Number 100017 Answers: 1 Comments: 0

(d^2 y/dx^2 ) + y = sec 3x

$$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:+\:\mathrm{y}\:=\:\mathrm{sec}\:\mathrm{3x}\: \\ $$

Question Number 100002 Answers: 0 Comments: 0

Question Number 100000 Answers: 2 Comments: 1

1+(1/(32))+(1/(243))+(1/(1024))+...∞

$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{32}}+\frac{\mathrm{1}}{\mathrm{243}}+\frac{\mathrm{1}}{\mathrm{1024}}+...\infty \\ $$

Question Number 99997 Answers: 0 Comments: 2

Question Number 99995 Answers: 0 Comments: 0

(√(1(√(3(√(5(√(7(√9)))))))))...∞

$$\sqrt{\mathrm{1}\sqrt{\mathrm{3}\sqrt{\mathrm{5}\sqrt{\mathrm{7}\sqrt{\mathrm{9}}}}}}...\infty \\ $$

Question Number 99994 Answers: 1 Comments: 0

1+(1/(16))+(1/(81))+(1/(256))+.....∞

$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{16}}+\frac{\mathrm{1}}{\mathrm{81}}+\frac{\mathrm{1}}{\mathrm{256}}+.....\infty \\ $$

Question Number 99992 Answers: 2 Comments: 0

y(1+x^3 )dy−x^2 dx = 0 ; y(2)=3

$$\mathrm{y}\left(\mathrm{1}+\mathrm{x}^{\mathrm{3}} \right)\mathrm{dy}−\mathrm{x}^{\mathrm{2}} \mathrm{dx}\:=\:\mathrm{0}\:;\:\mathrm{y}\left(\mathrm{2}\right)=\mathrm{3}\: \\ $$

Question Number 99989 Answers: 2 Comments: 0

(D^2 −4D+4)y = xe^(2x)

$$\left(\mathrm{D}^{\mathrm{2}} −\mathrm{4D}+\mathrm{4}\right)\mathrm{y}\:=\:{xe}^{\mathrm{2}{x}} \\ $$

Question Number 99986 Answers: 1 Comments: 0

Explain Einstein′s theory of Gravitation and explain why photons don′t fit Newton′s model but Einstein′s.

$$\mathrm{Explain}\:\mathrm{Einstein}'\mathrm{s}\:\mathrm{theory}\:\mathrm{of}\:\mathrm{Gravitation}\: \\ $$$$\mathrm{and}\:\mathrm{explain}\:\mathrm{why}\:\mathrm{photons}\:\mathrm{don}'\mathrm{t}\:\mathrm{fit}\:\mathrm{Newton}'\mathrm{s} \\ $$$$\mathrm{model}\:\mathrm{but}\:\mathrm{Einstein}'\mathrm{s}. \\ $$

Question Number 99985 Answers: 0 Comments: 0

A certain wire has length 4.5 cm and mass 12.3 g, with an electrical resistance of 1.1 mΩ. this wire falls through a horizontal magnetic field with flux density of 0.35 T. As his wire falls its ends slide smoothly between two rails connected by a wire with negligible internal resistance. Calculate the magnitude of the terminal energy resistance, neglecting the resistance of the rails.

$$\mathrm{A}\:\mathrm{certain}\:\mathrm{wire}\:\mathrm{has}\:\mathrm{length}\:\mathrm{4}.\mathrm{5}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{mass}\:\mathrm{12}.\mathrm{3}\:\mathrm{g},\:\:\mathrm{with}\:\mathrm{an} \\ $$$$\mathrm{electrical}\:\mathrm{resistance}\:\mathrm{of}\:\mathrm{1}.\mathrm{1}\:\mathrm{m}\Omega.\:\mathrm{this}\:\mathrm{wire}\:\mathrm{falls}\:\mathrm{through}\:\mathrm{a}\:\mathrm{horizontal} \\ $$$$\mathrm{magnetic}\:\mathrm{field}\:\:\mathrm{with}\:\mathrm{flux}\:\mathrm{density}\:\mathrm{of}\:\mathrm{0}.\mathrm{35}\:\mathrm{T}.\:\mathrm{As}\:\mathrm{his}\:\mathrm{wire}\:\mathrm{falls}\:\mathrm{its}\:\mathrm{ends} \\ $$$$\mathrm{slide}\:\mathrm{smoothly}\:\mathrm{between}\:\mathrm{two}\:\mathrm{rails}\:\mathrm{connected}\:\mathrm{by}\:\mathrm{a}\:\mathrm{wire}\:\mathrm{with}\:\mathrm{negligible} \\ $$$$\mathrm{internal}\:\mathrm{resistance}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{terminal}\:\mathrm{energy} \\ $$$$\mathrm{resistance},\:\mathrm{neglecting}\:\mathrm{the}\:\mathrm{resistance}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rails}. \\ $$

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