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Question Number 117416 Answers: 3 Comments: 0

lim_(x→∞) ((e^x^2 −cosx)/(sin^2 x))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } −\mathrm{cosx}}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}} \\ $$

Question Number 117414 Answers: 0 Comments: 0

Question Number 117412 Answers: 3 Comments: 2

lim_(x→(π/6)) ((1−2sin x)/( 1−(√3) tan x)) = ?

$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{6}}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{2sin}\:\mathrm{x}}{\:\mathrm{1}−\sqrt{\mathrm{3}}\:\mathrm{tan}\:\mathrm{x}}\:=\:? \\ $$

Question Number 117409 Answers: 1 Comments: 0

Question Number 117403 Answers: 1 Comments: 1

∫_0 ^1 (arc tan x)^2 dx =?

$$\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\left(\mathrm{arc}\:\mathrm{tan}\:\mathrm{x}\right)^{\mathrm{2}} \:\mathrm{dx}\:=? \\ $$

Question Number 117396 Answers: 3 Comments: 0

...differential equation... solve : (dy/dx)=(1/(xy+2x^2 y)) general solution =??? m.n.1970

$$\:\:\:\:\:\:\:\:...{differential}\:\:{equation}...\: \\ $$$$ \\ $$$$\:\:\:\:{solve}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{{dy}}{{dx}}=\frac{\mathrm{1}}{{xy}+\mathrm{2}{x}^{\mathrm{2}} {y}} \\ $$$$\:\:\:\:\:\:\:\:\:{general}\:\:{solution}\:=??? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$\: \\ $$

Question Number 117398 Answers: 0 Comments: 0

Question Number 117392 Answers: 2 Comments: 0

If log_4 x+(log_4 x)^2 +(log_4 x)^3 +(log_4 x)^4 +...=1 find the value of x.

$$\mathrm{If}\:\:\:\mathrm{log}_{\mathrm{4}} {x}+\left(\mathrm{log}_{\mathrm{4}} {x}\right)^{\mathrm{2}} +\left(\mathrm{log}_{\mathrm{4}} {x}\right)^{\mathrm{3}} +\left(\mathrm{log}_{\mathrm{4}} {x}\right)^{\mathrm{4}} +...=\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}. \\ $$

Question Number 117391 Answers: 1 Comments: 0

(√(2/3))−(√(2/(27)))+(√(2/(75)))−(√(2/(147)))+(√(2/(243)))−(√(2/(363)))+(√(2/(507)))−(√(2/(675)))+(√(2/(867)))−._ ...

$$\sqrt{\frac{\mathrm{2}}{\mathrm{3}}}−\sqrt{\frac{\mathrm{2}}{\mathrm{27}}}+\sqrt{\frac{\mathrm{2}}{\mathrm{75}}}−\sqrt{\frac{\mathrm{2}}{\mathrm{147}}}+\sqrt{\frac{\mathrm{2}}{\mathrm{243}}}−\sqrt{\frac{\mathrm{2}}{\mathrm{363}}}+\sqrt{\frac{\mathrm{2}}{\mathrm{507}}}−\sqrt{\frac{\mathrm{2}}{\mathrm{675}}}+\sqrt{\frac{\mathrm{2}}{\mathrm{867}}}−._{} ... \\ $$

Question Number 117388 Answers: 0 Comments: 0

Question Number 117387 Answers: 1 Comments: 1

Solve the trigonometric equation 5sinθ+3=0 for value of θ from 0° to 360°

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{trigonometric}\:\mathrm{equation} \\ $$$$\mathrm{5sin}\theta+\mathrm{3}=\mathrm{0}\:\mathrm{for}\:\mathrm{value}\:\mathrm{of}\:\theta\:\mathrm{from}\:\mathrm{0}°\:\mathrm{to} \\ $$$$\mathrm{360}° \\ $$

Question Number 117380 Answers: 1 Comments: 1

... prove that ... Ω=∫_0 ^( ∞) (1/(2(√x)))sin(π^2 x+(1/x))dx=(1/( (√(8π)))) m.n.1970

$$\:\:\:\:\:\:\:\:\:\:\:...\:\:{prove}\:\:{that}\:... \\ $$$$\:\: \\ $$$$\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}{sin}\left(\pi^{\mathrm{2}} {x}+\frac{\mathrm{1}}{{x}}\right){dx}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{8}\pi}} \\ $$$$ \\ $$$$\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$

Question Number 117371 Answers: 0 Comments: 0

Question Number 117369 Answers: 1 Comments: 0

Find the units digit of 2013^1 +2013^2 +2013^3 +...+2013^(2013)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{units}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{2013}^{\mathrm{1}} +\mathrm{2013}^{\mathrm{2}} +\mathrm{2013}^{\mathrm{3}} +...+\mathrm{2013}^{\mathrm{2013}} \\ $$

Question Number 117366 Answers: 0 Comments: 0

Σ_(n=1) ^∞ (((2n)!)/(n^(2n) n!(2n+1)))

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2}{n}\right)!}{{n}^{\mathrm{2}{n}} {n}!\left(\mathrm{2}{n}+\mathrm{1}\right)} \\ $$

Question Number 117365 Answers: 1 Comments: 1

Express ((1/2))! in terms of infinite series

$${Express}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\right)!\:\:{in}\:{terms}\:{of}\:{infinite}\:{series} \\ $$

Question Number 117348 Answers: 0 Comments: 1

Question Number 117344 Answers: 1 Comments: 4

Question Number 117342 Answers: 2 Comments: 0

(1)∫ (tan^(−1) (x))^2 dx = ? (2) ∫ tan^(−1) ((√x)) dx =?

$$\:\left(\mathrm{1}\right)\int\:\left(\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)\right)^{\mathrm{2}} \:\mathrm{dx}\:=\:? \\ $$$$\left(\mathrm{2}\right)\:\int\:\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\mathrm{x}}\right)\:\mathrm{dx}\:=? \\ $$

Question Number 117341 Answers: 0 Comments: 0

Question Number 117339 Answers: 1 Comments: 0

a coin tossed 8 times. Probability of appearing head at least 3 times is __

$${a}\:{coin}\:{tossed}\:\mathrm{8}\:{times}.\:{Probability} \\ $$$${of}\:{appearing}\:{head}\:{at}\:{least}\:\mathrm{3}\:{times}\:{is} \\ $$$$\_\_ \\ $$

Question Number 117329 Answers: 1 Comments: 0

nice math evaluate:: Ω=∫_0 ^( 1) ((arctan(x).ln(1−x))/(1+x^2 ))dx??? m.n.1970

$$\:\:\:\:\:\:\:\:\:{nice}\:\:{math} \\ $$$$\:\:{evaluate}:: \\ $$$$ \\ $$$$\:\:\:\: \\ $$$$\:\: \\ $$$$ \\ $$$$\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{arctan}\left({x}\right).{ln}\left(\mathrm{1}−{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}??? \\ $$$$\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$ \\ $$

Question Number 117311 Answers: 2 Comments: 0

Question Number 117299 Answers: 0 Comments: 2

Question Number 117281 Answers: 1 Comments: 0

In how many different ways can we select 5 numbers from 9 numbers {1,2,3,...,9}? A number may be selected more than one time.

$${In}\:{how}\:{many}\:{different}\:{ways}\:{can}\:{we} \\ $$$${select}\:\mathrm{5}\:{numbers}\:{from}\:\mathrm{9}\:{numbers} \\ $$$$\left\{\mathrm{1},\mathrm{2},\mathrm{3},...,\mathrm{9}\right\}?\: \\ $$$${A}\:{number}\:{may}\:{be}\:{selected}\:{more}\:{than} \\ $$$${one}\:{time}. \\ $$

Question Number 117280 Answers: 1 Comments: 0

... advanced calculus... prove that:: ∫_0 ^( 1) ln(Γ(x)).cos^2 (πx)dx =((ln(2π))/4)+(1/8) m.n.1970

$$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:{advanced}\:\:{calculus}...\: \\ $$$$ \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {ln}\left(\Gamma\left({x}\right)\right).{cos}^{\mathrm{2}} \left(\pi{x}\right){dx} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{{ln}\left(\mathrm{2}\pi\right)}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{8}} \\ $$$$\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$\: \\ $$

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