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Question Number 64762 Answers: 1 Comments: 1

Given that g(x)=(2/((1+x)(1+3x^2 )) a) express g(x) in partial fractions. b) evaluate ∫_0 ^1 g((x) dx.

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{g}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\left(\mathrm{1}+\mathrm{x}\right)\left(\mathrm{1}+\mathrm{3x}^{\mathrm{2}} \right.} \\ $$$$\left.\mathrm{a}\right)\:\mathrm{express}\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{in}\:\mathrm{partial}\:\mathrm{fractions}. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{evaluate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{g}\left(\left(\mathrm{x}\right)\:\mathrm{dx}.\right. \\ $$

Question Number 64759 Answers: 0 Comments: 0

∫((ln(ln(x)))/((ln(x))^n )) dx , n≠1

$$\int\frac{{ln}\left({ln}\left({x}\right)\right)}{\left({ln}\left({x}\right)\right)^{{n}} }\:{dx}\:\:\:,\:\:\:{n}\neq\mathrm{1} \\ $$

Question Number 64758 Answers: 2 Comments: 0

Solve: x^4 + 5x^3 − 4x^2 + 7x − 1 = 0

$$\mathrm{Solve}:\:\:\:\:\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{5x}^{\mathrm{3}} \:−\:\mathrm{4x}^{\mathrm{2}} \:+\:\mathrm{7x}\:−\:\mathrm{1}\:\:=\:\:\mathrm{0} \\ $$

Question Number 64751 Answers: 0 Comments: 1

Find the force parallel to the slope required to move a body of mass 2kg up a slope inclined at 30° to the horizontal with an acceleration oc 2m/s^2 if the frictional force is 10N.

$${Find}\:{the}\:{force}\:{parallel}\:{to}\:{the}\:{slope} \\ $$$${required}\:{to}\:{move}\:{a}\:{body}\:{of}\:{mass}\:\mathrm{2}{kg} \\ $$$${up}\:{a}\:{slope}\:{inclined}\:{at}\:\mathrm{30}°\:{to}\:{the} \\ $$$${horizontal}\:{with}\:{an}\:{acceleration}\:{oc}\:\mathrm{2}{m}/{s}^{\mathrm{2}} \\ $$$${if}\:{the}\:{frictional}\:{force}\:{is}\:\mathrm{10}{N}. \\ $$

Question Number 64750 Answers: 0 Comments: 0

A body of mass 4kg is at the point of slipping down a plane which is inclined at 30° to the horizontal.What is the force parallel to the plane that will just move it up?

$${A}\:{body}\:{of}\:{mass}\:\mathrm{4}{kg}\:{is}\:{at}\:{the}\:{point}\:{of} \\ $$$${slipping}\:{down}\:{a}\:{plane}\:{which}\:{is} \\ $$$${inclined}\:{at}\:\mathrm{30}°\:{to}\:{the}\:{horizontal}.{What} \\ $$$${is}\:{the}\:{force}\:{parallel}\:{to}\:{the}\:{plane}\:{that} \\ $$$${will}\:{just}\:{move}\:{it}\:{up}? \\ $$

Question Number 64745 Answers: 0 Comments: 1

calculate ∫_0 ^1 ((sin(lnx))/(lnx))dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{sin}\left({lnx}\right)}{{lnx}}{dx} \\ $$

Question Number 64744 Answers: 2 Comments: 0

solve^3 (√(1+x))+^3 (√(1−x))=2

$${solve}\:^{\mathrm{3}} \sqrt{\mathrm{1}+{x}}+^{\mathrm{3}} \sqrt{\mathrm{1}−{x}}=\mathrm{2} \\ $$

Question Number 64871 Answers: 0 Comments: 5

any hint about how to prove by induction in the Sigma notion topic? like in Σ

$${any}\:{hint}\:{about}\:{how}\:{to}\:{prove}\:{by}\:{induction}\:{in}\:{the}\:{Sigma}\:{notion}\:{topic}? \\ $$$${like}\:{in}\:\Sigma \\ $$

Question Number 64873 Answers: 0 Comments: 4

let f(x) =∫_0 ^π (dt/(x+sint)) with xreal 1) find a explicit form of f(x) 2) find also g(x) =∫_0 ^π (dt/((x+sint)^2 )) 3) give f^((n)) (x) at form of integral 4) calculate ∫_0 ^π (dt/(3+sint)) and ∫_0 ^π (dt/((3+sint)^2 ))

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dt}}{{x}+{sint}}\:\:\:{with}\:{xreal} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dt}}{\left({x}+{sint}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integral} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dt}}{\mathrm{3}+{sint}}\:\:{and}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dt}}{\left(\mathrm{3}+{sint}\right)^{\mathrm{2}} } \\ $$

Question Number 64872 Answers: 0 Comments: 4

Given that y = (cosx^ )^(sinx) find (dy/dx) and lim_(x→0) y

$${Given}\:{that}\: \\ $$$$\:{y}\:=\:\left({cosx}^{} \right)^{{sinx}} \:\:{find}\:\frac{{dy}}{{dx}} \\ $$$${and}\: \\ $$$$\:\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:{y} \\ $$

Question Number 64735 Answers: 0 Comments: 2

∫tanθ/1+^− sinθ dθ

$$\int{tan}\theta/\mathrm{1}\overset{−} {+}{sin}\theta\:{d}\theta \\ $$

Question Number 64733 Answers: 0 Comments: 0

∫(secθtanθ)dθ/secθ+^− tanθ

$$\int\left({sec}\theta{tan}\theta\right){d}\theta/{sec}\theta\overset{−} {+}{tan}\theta \\ $$

Question Number 64730 Answers: 2 Comments: 0

Question Number 64729 Answers: 0 Comments: 0

Question Number 64728 Answers: 0 Comments: 0

Question Number 64726 Answers: 0 Comments: 0

Question Number 64709 Answers: 1 Comments: 1

Question Number 64702 Answers: 1 Comments: 0

Question Number 64697 Answers: 1 Comments: 0

i need some help here. An object of mass m falls from a height h_1 and rebound to a height of h_2 . write an expression for its momentum.

$${i}\:{need}\:{some}\:{help}\:{here}.\: \\ $$$$\:{An}\:{object}\:{of}\:{mass}\:\:\:{m}\:\:\:{falls}\:{from}\:{a}\:{height}\:\:{h}_{\mathrm{1}} \:{and}\:{rebound} \\ $$$${to}\:{a}\:{height}\:{of}\:{h}_{\mathrm{2}} .\:{write}\:{an}\:{expression}\:{for}\:{its}\:{momentum}. \\ $$

Question Number 64698 Answers: 1 Comments: 4

Question Number 64688 Answers: 1 Comments: 0

Question Number 64687 Answers: 0 Comments: 1

Question Number 64686 Answers: 1 Comments: 0

Question Number 64677 Answers: 0 Comments: 4

let f(x) =∫_0 ^1 lnt ln(1−xt)dt with ∣x∣<1 1)determine a explicit form for f(x) 2) find also g(x) =∫_0 ^1 ((tlnt)/(1−xt))dt 3) give f^((n)) (x) at form of integral 4) calculate ∫_0 ^1 ln(t)ln(1−t)dt and ∫_0 ^1 ln(t)ln(2−t)dt 5) calculate ∫_0 ^1 ((tln(t))/(2−t)) dt .

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {lnt}\:{ln}\left(\mathrm{1}−{xt}\right){dt}\:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right){determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{tlnt}}{\mathrm{1}−{xt}}{dt} \\ $$$$\left.\mathrm{3}\right)\:{give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integral} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({t}\right){ln}\left(\mathrm{1}−{t}\right){dt}\:\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left({t}\right){ln}\left(\mathrm{2}−{t}\right){dt} \\ $$$$\left.\mathrm{5}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{tln}\left({t}\right)}{\mathrm{2}−{t}}\:{dt}\:. \\ $$

Question Number 64676 Answers: 0 Comments: 0

z^4 −12iz−100=0

$${z}^{\mathrm{4}} −\mathrm{12}{iz}−\mathrm{100}=\mathrm{0} \\ $$

Question Number 64662 Answers: 1 Comments: 3

∫(dx/((x^8 +x^4 +1)^2 )) ∫_(1/x) ^x ((ln(t))/(t^2 +1)) dt

$$\int\frac{{dx}}{\left({x}^{\mathrm{8}} +{x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$\int_{\frac{\mathrm{1}}{{x}}} ^{{x}} \frac{{ln}\left({t}\right)}{{t}^{\mathrm{2}} +\mathrm{1}}\:{dt} \\ $$

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