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Question Number 68329 Answers: 0 Comments: 0

y=ln (sinx+x^2 )

$${y}=\mathrm{ln}\:\left({sinx}+{x}^{\mathrm{2}} \right) \\ $$

Question Number 68327 Answers: 1 Comments: 0

y=(1−2x^(−7) )^3

$${y}=\left(\mathrm{1}−\mathrm{2}{x}^{−\mathrm{7}} \right)^{\mathrm{3}} \\ $$

Question Number 68316 Answers: 0 Comments: 1

∫(4sin 3x+(e^(4x) /4))

$$\int\left(\mathrm{4sin}\:\mathrm{3}{x}+\frac{{e}^{\mathrm{4}{x}} }{\mathrm{4}}\right) \\ $$

Question Number 68315 Answers: 0 Comments: 1

∫(((x^(−3) +2x−4)/x))

$$\int\left(\frac{{x}^{−\mathrm{3}} +\mathrm{2}{x}−\mathrm{4}}{{x}}\right) \\ $$

Question Number 68309 Answers: 1 Comments: 3

Question Number 68313 Answers: 0 Comments: 1

∫(1−(6/x)+(2/x^2 )+(√x))

$$\int\left(\mathrm{1}−\frac{\mathrm{6}}{{x}}+\frac{\mathrm{2}}{{x}^{\mathrm{2}} }+\sqrt{{x}}\right) \\ $$

Question Number 68305 Answers: 1 Comments: 3

Question Number 68303 Answers: 0 Comments: 0

Question Number 68308 Answers: 1 Comments: 0

solve y′′′=y′′y′

$${solve}\:{y}'''={y}''{y}' \\ $$

Question Number 68294 Answers: 0 Comments: 0

Question Number 68285 Answers: 1 Comments: 2

two students ngum ebon gave their ages as 124_4 and 33_x respectively.if both of them are of thesame ages .find in what base ebon gave her age

$${two}\:{students}\:{ngum}\:{ebon}\:{gave}\:{their}\:{ages}\:{as}\:\mathrm{124}_{\mathrm{4}} {and}\:\mathrm{33}_{{x}} {respectively}.{if}\:{both}\:{of}\:{them}\:{are}\:{of}\:{thesame}\:{ages}\:.{find}\:{in}\:{what}\:{base}\:{ebon}\:{gave}\:{her}\:{age} \\ $$

Question Number 68280 Answers: 1 Comments: 1

given that 432_n −413_n =11_(10) .find the value of n

$${given}\:{that}\:\mathrm{432}_{{n}} −\mathrm{413}_{{n}} =\mathrm{11}_{\mathrm{10}} .{find}\:{the}\:{value}\:{of}\:{n} \\ $$

Question Number 68289 Answers: 1 Comments: 0

A circle is divided into two equal parts By An arc with center on the circle. Determine (a) The length of the arc (b)The ratio in which the arc divides the diameter meeting the center of the arc.

$$\mathrm{A}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{two}\:\mathrm{equal}\:\mathrm{parts} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{By} \\ $$$$\:\mathrm{An}\:\mathrm{arc}\:\mathrm{with}\:\mathrm{center}\:\mathrm{on}\:\mathrm{the}\:\mathrm{circle}. \\ $$$$\mathcal{D}{etermine} \\ $$$$\:\:\left({a}\right)\:{The}\:{length}\:{of}\:{the}\:{arc} \\ $$$$\:\:\left({b}\right){The}\:{ratio}\:{in}\:{which}\:{the}\:{arc} \\ $$$$\:\:\:\:\:\:\:\:{divides}\:{the}\:{diameter}\: \\ $$$$\:\:\:\:\:\:\:\:{meeting}\:{the}\:{center}\:{of}\:{the}\:{arc}. \\ $$

Question Number 68272 Answers: 1 Comments: 0

Question Number 68271 Answers: 0 Comments: 0

Find J=∫_0 ^1 ((W(−ulnu))/(ulnu)) du when W is the lambert function

$$\:\:{Find}\:\:{J}=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{W}\left(−{ulnu}\right)}{{ulnu}}\:{du}\:\:\:\:{when}\:\:{W}\:{is}\:{the}\:{lambert}\:{function} \\ $$

Question Number 68270 Answers: 1 Comments: 3

Prove that if Li_2 (x)=Σ_(n=1) (x^n /n^2 ) then ∀ x Li_2 (x)+Li_2 (1−x) = (π^2 /6) −ln(x)ln(1−x) ∀ x∉[0:1] Li_2 (x)+Li_2 ((1/x)) = −(π^2 /6) −[ln(−x)]^2 Find A=Σ_(n=1) ^∞ (ϕ^n /n^2 ) and B=Σ_(n=1) ^∞ (2^n /n^2 )

$$\:{Prove}\:{that}\:\:{if}\:\:{Li}_{\mathrm{2}} \left({x}\right)=\underset{{n}=\mathrm{1}} {\sum}\:\frac{{x}^{{n}} }{{n}^{\mathrm{2}} }\:\:\:{then} \\ $$$$\forall\:{x}\:\:{Li}_{\mathrm{2}} \left({x}\right)+{Li}_{\mathrm{2}} \left(\mathrm{1}−{x}\right)\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}}\:−{ln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right)\:\: \\ $$$$\forall\:{x}\notin\left[\mathrm{0}:\mathrm{1}\right]\:{Li}_{\mathrm{2}} \left({x}\right)+{Li}_{\mathrm{2}} \left(\frac{\mathrm{1}}{{x}}\right)\:=\:−\frac{\pi^{\mathrm{2}} }{\mathrm{6}}\:−\left[{ln}\left(−{x}\right)\right]^{\mathrm{2}} \:\: \\ $$$${Find}\:\:{A}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\varphi^{{n}} }{{n}^{\mathrm{2}} }\:\:{and}\:\:{B}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{2}^{{n}} }{{n}^{\mathrm{2}} }\:\: \\ $$

Question Number 68260 Answers: 0 Comments: 1

find f(x) if f((1/x))+f(1−x)=x

$${find}\:{f}\left({x}\right)\:{if}\: \\ $$$${f}\left(\frac{\mathrm{1}}{{x}}\right)+{f}\left(\mathrm{1}−{x}\right)={x} \\ $$

Question Number 68278 Answers: 0 Comments: 2

Question Number 68257 Answers: 0 Comments: 0

Prove that (6/(673)) Σ_(n=1) ^∞ (1/(n^2 (((2n)),(n) ))) = (π^2 /(2019))

$$\:\:{Prove}\:{that}\:\:\frac{\mathrm{6}}{\mathrm{673}}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}}\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{2019}}\: \\ $$

Question Number 68244 Answers: 0 Comments: 1

find nature of the serie Σ_(n=1) ^∞ arctan(n+(1/n))

$${find}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{arctan}\left({n}+\frac{\mathrm{1}}{{n}}\right) \\ $$

Question Number 68243 Answers: 0 Comments: 3

let f(x) =arctan(ax +1) with a real 1) calculate f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie 3) calculate ∫_(−∞) ^(+∞) ((f(x))/(x^2 +4))dx

$${let}\:{f}\left({x}\right)\:={arctan}\left({ax}\:+\mathrm{1}\right)\:\:{with}\:{a}\:{real} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{{f}\left({x}\right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}{dx} \\ $$

Question Number 68242 Answers: 0 Comments: 0

find lim_(x→0) ((cos(πx^x )+1)/x^2 )

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{cos}\left(\pi{x}^{{x}} \right)+\mathrm{1}}{{x}^{\mathrm{2}} } \\ $$

Question Number 68241 Answers: 0 Comments: 1

calculate ∫∫_w (x^2 −2y^2 )(√(x^2 +3y^2 ))dxdy with w ={(x,y)∈R^2 / 0≤x≤1 and 1≤y≤2}

$${calculate}\:\int\int_{{w}} \:\:\:\left({x}^{\mathrm{2}} −\mathrm{2}{y}^{\mathrm{2}} \right)\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} }{dxdy} \\ $$$${with}\:{w}\:=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:\:{and}\:\mathrm{1}\leqslant{y}\leqslant\mathrm{2}\right\} \\ $$

Question Number 68240 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((arctan(3x)−arctan(2x))/x)dx

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{3}{x}\right)−{arctan}\left(\mathrm{2}{x}\right)}{{x}}{dx} \\ $$

Question Number 68239 Answers: 0 Comments: 2

let f(x) =e^(−2x) ln(1+x^2 ) developp f at integr serie.

$${let}\:{f}\left({x}\right)\:={e}^{−\mathrm{2}{x}} {ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right) \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 68238 Answers: 0 Comments: 2

let f(x)=(x^2 −3x)arctan(2x+1) 1) determine f^((n)) (x) and f^((n)) (0) 2)developp f at integr serie 3) calculate ∫_0 ^1 f(x)dx

$${let}\:\:{f}\left({x}\right)=\left({x}^{\mathrm{2}} −\mathrm{3}{x}\right){arctan}\left(\mathrm{2}{x}+\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{f}^{\left({n}\right)} \left({x}\right)\:\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx} \\ $$

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