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Question Number 36851 Answers: 1 Comments: 0

Question Number 36855 Answers: 1 Comments: 1

Question Number 36846 Answers: 1 Comments: 6

Question Number 36845 Answers: 0 Comments: 0

Question Number 36844 Answers: 1 Comments: 0

find the sum of 4 digit even numbers formed from the digit 1, 2, 3, 4

$$\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{4}\:\mathrm{digit}\:\mathrm{even}\:\mathrm{numbers}\:\mathrm{formed}\:\mathrm{from}\:\mathrm{the}\:\mathrm{digit}\:\:\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4} \\ $$

Question Number 36843 Answers: 1 Comments: 1

lim_(x→∞) (x^x^x^(.....) )

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left({x}^{{x}^{{x}^{.....} } } \right) \\ $$

Question Number 36837 Answers: 1 Comments: 1

Σ_(r=0) ^∞ 2^(4r−2)

$$\underset{{r}=\mathrm{0}} {\overset{\infty} {\sum}}\mathrm{2}^{\mathrm{4}{r}−\mathrm{2}} \: \\ $$

Question Number 36828 Answers: 0 Comments: 7

Question Number 36821 Answers: 2 Comments: 1

>. 2sin((5π)/(12))sin(π/(12)) slove this.?

$$>.\:\mathrm{2}{sin}\frac{\mathrm{5}\pi}{\mathrm{12}}{sin}\frac{\pi}{\mathrm{12}}\:{slove}\:{this}.? \\ $$

Question Number 36820 Answers: 1 Comments: 1

find the value of Σ_(n=2) ^∞ (1/((n−1)^2 (n+1)^2 ))

$${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\frac{\mathrm{1}}{\left({n}−\mathrm{1}\right)^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{2}} }\: \\ $$

Question Number 36819 Answers: 0 Comments: 1

find the value of the sum Σ_(n=1) ^∞ (1/((2n−1)^2 (2n+1)^2 ))

$${find}\:{the}\:{value}\:{of}\:{the}\:{sum}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\mathrm{1}}{\left(\mathrm{2}{n}−\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 36818 Answers: 1 Comments: 1

find f(a) = ∫ (dx/(√(1−ax^2 ))) with a from R .

$${find}\:{f}\left({a}\right)\:=\:\int\:\:\:\:\:\frac{{dx}}{\sqrt{\mathrm{1}−{ax}^{\mathrm{2}} }}\:\:{with}\:{a}\:{from}\:{R}\:. \\ $$

Question Number 36814 Answers: 1 Comments: 0

now the way is clear, also try this one: ∫((cos x)/(sin^2 x (√(sin 2x))))dx

$$\mathrm{now}\:\mathrm{the}\:\mathrm{way}\:\mathrm{is}\:\mathrm{clear},\:\mathrm{also}\:\mathrm{try}\:\mathrm{this}\:\mathrm{one}: \\ $$$$\int\frac{\mathrm{cos}\:{x}}{\mathrm{sin}^{\mathrm{2}} \:{x}\:\sqrt{\mathrm{sin}\:\mathrm{2}{x}}}{dx} \\ $$

Question Number 36811 Answers: 1 Comments: 0

∫ ((sin x)/(cos^2 x. (√(cos 2x)))) dx= ?

$$\int\:\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:^{\mathrm{2}} {x}.\:\sqrt{\mathrm{cos}\:\mathrm{2}{x}}}\:{dx}=\:? \\ $$

Question Number 36801 Answers: 2 Comments: 0

∫ ((1+x^4 )/((1−x^4 )^(3/2) )) dx = A ∫ A = B Find B ? Assume integration of constant=0.

$$\int\:\frac{\mathrm{1}+{x}^{\mathrm{4}} }{\left(\mathrm{1}−{x}^{\mathrm{4}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} }\:{dx}\:=\:{A}\: \\ $$$$\int\:\mathrm{A}\:=\:\mathrm{B} \\ $$$$\mathrm{Find}\:\mathrm{B}\:? \\ $$$$\mathrm{Assume}\:\mathrm{integration}\:\mathrm{of}\:\mathrm{constant}=\mathrm{0}. \\ $$

Question Number 36799 Answers: 1 Comments: 1

find ∫_0 ^∞ e^t ln(1+e^(−2t) )dt .

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:{e}^{{t}} {ln}\left(\mathrm{1}+{e}^{−\mathrm{2}{t}} \right){dt}\:. \\ $$

Question Number 36784 Answers: 0 Comments: 0

Prove that Σ_(r=0) ^n r ((n),(r) )^2 = n (((2n − 1)),(( n − 1)) )

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:{r}\:\begin{pmatrix}{{n}}\\{{r}}\end{pmatrix}^{\mathrm{2}} \:=\:{n}\:\begin{pmatrix}{\mathrm{2}{n}\:−\:\mathrm{1}}\\{\:\:{n}\:−\:\mathrm{1}}\end{pmatrix} \\ $$

Question Number 36771 Answers: 0 Comments: 3

i have a suggestion...pls request members of the forum to post four to five question so that we get time to solve them...there is flood of questions...so little time to see all post pls give comment if you agree wkth it...

$${i}\:{have}\:{a}\:{suggestion}...{pls}\:{request}\:{members} \\ $$$${of}\:{the}\:{forum}\:{to}\:{post}\:{four}\:{to}\:{five}\:{question} \\ $$$${so}\:{that}\:{we}\:{get}\:{time}\:{to}\:{solve}\:{them}...{there}\:{is}\: \\ $$$${flood}\:{of}\:{questions}...{so}\:{little}\:{time}\:{to}\:{see}\:{all}\:{post} \\ $$$${pls}\:{give}\:{comment}\:{if}\:{you}\:{agree}\:{wkth}\:{it}... \\ $$

Question Number 36762 Answers: 1 Comments: 2

find A_n = ∫_0 ^(π/4) (cosx +sinx)^n dx.

$${find}\:{A}_{{n}} \:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\left({cosx}\:+{sinx}\right)^{{n}} \:{dx}. \\ $$

Question Number 36755 Answers: 1 Comments: 4

let f(a) = ∫_0 ^1 e^t ln(1+ e^(−at) )dt with a≥0 1) find f(a) 2) calculate f^′ (a) 3) find the value of ∫_0 ^1 e^t ln(1+e^(−3t) )dt .

$${let}\:{f}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{e}^{{t}} {ln}\left(\mathrm{1}+\:{e}^{−{at}} \right){dt}\:\:{with}\:{a}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({a}\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{{t}} {ln}\left(\mathrm{1}+{e}^{−\mathrm{3}{t}} \right){dt}\:. \\ $$

Question Number 36754 Answers: 1 Comments: 1

calculate ∫_1 ^(+∞) (dx/(x^2 (√(4+x^2 )))) .

$${calculate}\:\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \sqrt{\mathrm{4}+{x}^{\mathrm{2}} }}\:. \\ $$

Question Number 36753 Answers: 1 Comments: 2

find I_n = ∫_0 ^1 x^n arctan(x)dx .

$${find}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:{x}^{{n}} \:{arctan}\left({x}\right){dx}\:. \\ $$

Question Number 36752 Answers: 1 Comments: 4

find ∫ (dx/(arcsinx(√(1−x^2 )))) .

$${find}\:\:\int\:\:\:\frac{{dx}}{{arcsinx}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:. \\ $$

Question Number 36751 Answers: 0 Comments: 0

let f(x)= Σ_(n=1) ^∞ x^n^2 with x∈]−1,1[ prove that f(x) ∼ ((√π)/(2(√(−ln(x))))) (x →1^− )

$$\left.{let}\:\:{f}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{x}^{{n}^{\mathrm{2}} } \:\:\:{with}\:\:{x}\in\right]−\mathrm{1},\mathrm{1}\left[\right. \\ $$$${prove}\:{that}\:\:{f}\left({x}\right)\:\sim\:\frac{\sqrt{\pi}}{\mathrm{2}\sqrt{−{ln}\left({x}\right)}}\:\left({x}\:\rightarrow\mathrm{1}^{−} \right) \\ $$

Question Number 36750 Answers: 0 Comments: 0

let f(t)=Σ_(n≥1) (−1)^n ln{1+ (t^2 /(n(1+t^2 )))} 1) study the simple and uniform convergence of Σ f_n 2)study the continuity of f 3) prove that lim_(t→+∞) f(t)=ln((2/π)) .

$${let}\:{f}\left({t}\right)=\sum_{{n}\geqslant\mathrm{1}} \:\left(−\mathrm{1}\right)^{{n}} {ln}\left\{\mathrm{1}+\:\frac{{t}^{\mathrm{2}} }{{n}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}\right\} \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{simple}\:\:{and}\:{uniform}\:{convergence} \\ $$$${of}\:\Sigma\:{f}_{{n}} \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{continuity}\:{of}\:{f} \\ $$$$\left.\mathrm{3}\right)\:{prove}\:{that}\:{lim}_{{t}\rightarrow+\infty} \:{f}\left({t}\right)={ln}\left(\frac{\mathrm{2}}{\pi}\right)\:. \\ $$

Question Number 36748 Answers: 0 Comments: 0

let f(x)= Σ_(n=1) ^∞ (((−1)^(n−1) )/(ln(nx))) 1) give D_f and study f on]1,+∞[ 2)study the continjity of f and calculate lim _(x→1) f(x) and lim_(x→+∞) f(x). 3) prove that f is C^1 on ]1,+∞[ .

$${let}\:{f}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{ln}\left({nx}\right)} \\ $$$$\left.\mathrm{1}\left.\right)\:{give}\:{D}_{{f}} \:\:{and}\:{study}\:{f}\:{on}\right]\mathrm{1},+\infty\left[\right. \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{continjity}\:{of}\:{f}\:{and}\:{calculate} \\ $$$${lim}\:_{{x}\rightarrow\mathrm{1}} {f}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right). \\ $$$$\left.\mathrm{3}\left.\right)\:{prove}\:{that}\:{f}\:{is}\:{C}^{\mathrm{1}} \:{on}\:\right]\mathrm{1},+\infty\left[\:.\right. \\ $$

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