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Question Number 64525 Answers: 0 Comments: 1

study the convergence of Σ U_n with U_n =∫_0 ^∞ ((cos(nx))/(x^2 +n^2 ))dx (n≥1)

$${study}\:{the}\:{convergence}\:{of}\:\Sigma\:{U}_{{n}} \:\:\:{with} \\ $$$${U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({nx}\right)}{{x}^{\mathrm{2}} \:+{n}^{\mathrm{2}} }{dx}\:\:\:\left({n}\geqslant\mathrm{1}\right) \\ $$

Question Number 64522 Answers: 1 Comments: 0

In a hospital, Dr Steve has worked more night shifts than Dr Gregg who has worked five night shifts. Dr Okon has worked 15 night shifts more than Dr Steve and Dr Gregg combined. Dr. Uche has worked eight night shifts less than Dr Steve.How many night shifts has Dr. Steve worked? a)10 b)9 c)8 d)7

$${In}\:{a}\:{hospital},\:{Dr}\:{Steve}\:{has}\:{worked} \\ $$$${more}\:{night}\:{shifts}\:{than}\:{Dr}\:{Gregg}\:{who} \\ $$$${has}\:{worked}\:{five}\:{night}\:{shifts}.\:{Dr}\:{Okon} \\ $$$${has}\:{worked}\:\mathrm{15}\:{night}\:{shifts}\:{more}\:{than} \\ $$$${Dr}\:{Steve}\:{and}\:{Dr}\:{Gregg}\:{combined}. \\ $$$${Dr}.\:{Uche}\:{has}\:{worked}\:{eight}\:{night}\:{shifts} \\ $$$${less}\:{than}\:{Dr}\:{Steve}.{How}\:{many}\:{night} \\ $$$${shifts}\:{has}\:{Dr}.\:{Steve}\:{worked}? \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left.\mathrm{0}\:{b}\right)\mathrm{9}\:{c}\right)\mathrm{8}\:{d}\right)\mathrm{7} \\ $$

Question Number 64519 Answers: 1 Comments: 0

a,b,c is a geometric progression such that a+b+c=26 a^2 +b^2 +c^2 =364 find a,b,c

$${a},{b},{c}\:{is}\:{a}\:{geometric}\:{progression}\:{such} \\ $$$${that} \\ $$$${a}+{b}+{c}=\mathrm{26} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{364} \\ $$$$ \\ $$$${find}\:{a},{b},{c} \\ $$

Question Number 64516 Answers: 2 Comments: 5

Question Number 64514 Answers: 0 Comments: 2

y=arc tan[(√((1−cosx)/(1+cosx)))] y^ =?

$${y}={arc}\:{tan}\left[\sqrt{\frac{\mathrm{1}−{cosx}}{\mathrm{1}+{cosx}}}\right] \\ $$$${y}^{} =? \\ $$

Question Number 64498 Answers: 0 Comments: 0

please, anyone help me to solve this i. Σ_(k=1) ^n cos(((k^2 π)/n)) ii. Σ_(k=1) ^(n) sin(((k^2 π)/n)) thank you.

$$\mathrm{please},\:\mathrm{anyone}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this} \\ $$$$\mathrm{i}.\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{cos}\left(\frac{\mathrm{k}^{\mathrm{2}} \pi}{\mathrm{n}}\right) \\ $$$$\mathrm{ii}.\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\Sigma}}\mathrm{sin}\left(\frac{\mathrm{k}^{\mathrm{2}} \pi}{\mathrm{n}}\right) \\ $$$$\mathrm{thank}\:\mathrm{you}. \\ $$

Question Number 64508 Answers: 2 Comments: 1

factorize (x+1)(x+3)(x+5)(x+7)+16

$$\mathrm{factorize}\:\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}+\mathrm{3}\right)\left(\mathrm{x}+\mathrm{5}\right)\left(\mathrm{x}+\mathrm{7}\right)+\mathrm{16} \\ $$

Question Number 64478 Answers: 1 Comments: 2

Question Number 64477 Answers: 0 Comments: 1

pls i need it urgently... am stuck workings please (1) ∫Ln(1−Lnx)dx (2) ∫(1/(Lnx))dx (3)∫ Ln(−2Lnx)dx God will honour u 4 ur replies

$${pls}\:\:{i}\:{need}\:{it}\:{urgently}...\:{am}\:{stuck} \\ $$$${workings}\:{please} \\ $$$$\left(\mathrm{1}\right)\:\:\int{Ln}\left(\mathrm{1}−{Lnx}\right){dx} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:\:\int\frac{\mathrm{1}}{{Lnx}}{dx} \\ $$$$ \\ $$$$\left(\mathrm{3}\right)\int\:{Ln}\left(−\mathrm{2}{Lnx}\right){dx} \\ $$$$ \\ $$$${God}\:{will}\:{honour}\:{u}\:\mathrm{4}\:{ur}\:{replies} \\ $$

Question Number 64475 Answers: 2 Comments: 6

solve the equation sin(x)+sin(2x)+sin(3x)=cos(x)+cos(2x)+cos(3x)

$${solve}\:{the}\:{equation} \\ $$$${sin}\left({x}\right)+{sin}\left(\mathrm{2}{x}\right)+{sin}\left(\mathrm{3}{x}\right)={cos}\left({x}\right)+{cos}\left(\mathrm{2}{x}\right)+{cos}\left(\mathrm{3}{x}\right) \\ $$

Question Number 64471 Answers: 1 Comments: 0

∫((tanx))^(1/4) dx

$$\int\sqrt[{\mathrm{4}}]{{tanx}}{dx} \\ $$

Question Number 64469 Answers: 1 Comments: 0

Question Number 64465 Answers: 0 Comments: 0

$${vy} \\ $$

Question Number 64463 Answers: 0 Comments: 1

∫(√(sec(x))) dx

$$\int\sqrt{{sec}\left({x}\right)}\:{dx} \\ $$

Question Number 64459 Answers: 0 Comments: 2

Question Number 64452 Answers: 1 Comments: 5

Question Number 64456 Answers: 0 Comments: 1

Question Number 64448 Answers: 1 Comments: 1

calculate lim_(x→π) ∫_(π/2) ^x (dx/(1+sinx−cosx))

$${calculate}\:{lim}_{{x}\rightarrow\pi} \:\:\int_{\frac{\pi}{\mathrm{2}}} ^{{x}} \:\:\:\frac{{dx}}{\mathrm{1}+{sinx}−{cosx}} \\ $$

Question Number 64447 Answers: 1 Comments: 0

Question Number 64445 Answers: 0 Comments: 0

calculate W_n =Σ_(1≤i≤j≤n) i×j

$${calculate}\:\:{W}_{{n}} =\sum_{\mathrm{1}\leqslant{i}\leqslant{j}\leqslant{n}} \:{i}×{j} \\ $$

Question Number 64444 Answers: 0 Comments: 2

calculate A_n =Σ_(k=0) ^n (k/((k+1)!))

$${calculate}\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{{k}}{\left({k}+\mathrm{1}\right)!} \\ $$

Question Number 64443 Answers: 0 Comments: 0

find all functin f Z→Z wich verify ∀(a,b)∈Z^2 f(2a)+2f(b) =f(f(a+b))

$${find}\:{all}\:{functin}\:{f}\:{Z}\rightarrow{Z}\:\:{wich}\:{verify} \\ $$$$\forall\left({a},{b}\right)\in{Z}^{\mathrm{2}} \:\:\:\:\:{f}\left(\mathrm{2}{a}\right)+\mathrm{2}{f}\left({b}\right)\:={f}\left({f}\left({a}+{b}\right)\right) \\ $$

Question Number 64436 Answers: 2 Comments: 1

Question Number 64429 Answers: 0 Comments: 5

let f(x)=∫_0 ^1 (dt/(t+x+(√(t^2 +1)))) (x real parametre) 1) find a explicite form forf(x) 2)detemine also g(x) =∫_0 ^1 (dt/((t+x+(√(t^2 +1)))^2 )) 3)give f^((n)) (x) at form of integrals 4) find the values of ∫_0 ^1 (dt/(t+(√(t^2 +1)))) and ∫_0 ^1 (dt/((t+(√(t^2 +1)))^2 )) 5) find the values of ∫_0 ^1 (dt/(t+1 +(√(t^2 +1)))) and ∫_0 ^1 (dt/((t+1+(√(t^2 +1)))^2 ))

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{{t}+{x}+\sqrt{{t}^{\mathrm{2}} \:+\mathrm{1}}}\:\:\:\left({x}\:{real}\:{parametre}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicite}\:{form}\:{forf}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){detemine}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\left({t}+{x}+\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right){give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integrals} \\ $$$$\left.\mathrm{4}\right)\:{find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{{t}+\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}}\:\:{and}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\left({t}+\sqrt{{t}^{\mathrm{2}} \:+\mathrm{1}}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{5}\right)\:{find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{{t}+\mathrm{1}\:+\sqrt{{t}^{\mathrm{2}} \:+\mathrm{1}}}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\left({t}+\mathrm{1}+\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}\right)^{\mathrm{2}} } \\ $$

Question Number 64425 Answers: 0 Comments: 4

Question Number 64419 Answers: 0 Comments: 1

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

$$\left.\mathrm{1}\right)\:{find}\:\int\:\:\frac{{dx}}{{x}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{{x}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \\ $$

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