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Question Number 90630 Answers: 1 Comments: 1

f(x) = xe^(−x) f^((2020)) (x) =

$${f}\left({x}\right)\:=\:{xe}^{−{x}} \\ $$$${f}^{\left(\mathrm{2020}\right)} \left({x}\right)\:=\: \\ $$

Question Number 90629 Answers: 1 Comments: 1

If sin^(−1) (1−x)−2 sin^(−1) x = (π/2), then x=

$$\mathrm{If}\:\:\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{1}−{x}\right)−\mathrm{2}\:\mathrm{sin}^{−\mathrm{1}} {x}\:=\:\frac{\pi}{\mathrm{2}},\:\mathrm{then}\:{x}= \\ $$

Question Number 90628 Answers: 0 Comments: 1

The value of sin (π/(14)) sin ((3π)/(14)) sin ((5π)/(14)) is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}\:\frac{\pi}{\mathrm{14}}\:\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{14}}\:\mathrm{sin}\:\frac{\mathrm{5}\pi}{\mathrm{14}}\:\:\mathrm{is} \\ $$

Question Number 90625 Answers: 0 Comments: 0

∫e^(arcsinx) dx

$$\int{e}^{{arcsinx}} {dx} \\ $$

Question Number 90609 Answers: 0 Comments: 3

find the infinite sumΣ_(n=0) ^∞ (F_n /2^n ) where F_n =(1/(√5))(((1+(√5))/2))^(n+1) −(1/(√5))(((1−(√5))/2))^(n+1)

$${find}\:{the}\:{infinite}\:{sum}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{F}_{{n}} }{\mathrm{2}^{{n}} }\: \\ $$$${where}\:{F}_{{n}} =\frac{\mathrm{1}}{\sqrt{\mathrm{5}}}\left(\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\right)^{{n}+\mathrm{1}} −\frac{\mathrm{1}}{\sqrt{\mathrm{5}}}\left(\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}\right)^{{n}+\mathrm{1}} \\ $$

Question Number 90596 Answers: 1 Comments: 0

If sin(28) = a and cos(32) = b Find (i) cos(28) (ii) cos(64) (iii) sin(4)

$$\mathrm{If}\:\:\:\mathrm{sin}\left(\mathrm{28}\right)\:\:=\:\:\mathrm{a}\:\:\:\:\mathrm{and}\:\:\:\mathrm{cos}\left(\mathrm{32}\right)\:\:=\:\:\mathrm{b} \\ $$$$\mathrm{Find}\:\:\left(\mathrm{i}\right)\:\:\mathrm{cos}\left(\mathrm{28}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{ii}\right)\:\mathrm{cos}\left(\mathrm{64}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{iii}\right)\:\mathrm{sin}\left(\mathrm{4}\right) \\ $$

Question Number 90594 Answers: 0 Comments: 3

Question Number 90592 Answers: 0 Comments: 3

∫_0 ^(√(arccos(((−2φ)/π)+1))) x sin(x^2 ) dx

$$\int_{\mathrm{0}} ^{\sqrt{{arccos}\left(\frac{−\mathrm{2}\phi}{\pi}+\mathrm{1}\right)}} {x}\:{sin}\left({x}^{\mathrm{2}} \right)\:{dx} \\ $$

Question Number 90590 Answers: 1 Comments: 2

Question Number 90589 Answers: 0 Comments: 3

∫(1/(x+(√(x^2 +x+1))))dx

$$\int\frac{\mathrm{1}}{{x}+\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}{dx} \\ $$

Question Number 90588 Answers: 1 Comments: 0

∫(√(x+(√(x^2 +6 ))))dx

$$\int\sqrt{{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{6}\:\:}}{dx} \\ $$

Question Number 90575 Answers: 0 Comments: 0

Solve the differential equation: x y_3 +(1−2x^2 )y_2 −8x _ y_1 −4y= e^x

$$\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{y}}_{\mathrm{3}} +\left(\mathrm{1}−\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)\boldsymbol{\mathrm{y}}_{\mathrm{2}} −\mathrm{8}\boldsymbol{\mathrm{x}}\:_{\:} \boldsymbol{\mathrm{y}}_{\mathrm{1}} −\mathrm{4}\boldsymbol{\mathrm{y}}=\:\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} \\ $$

Question Number 90574 Answers: 0 Comments: 2

Use gamma function to prove (i) . ∫_0 ^( (𝛑/8)) cos^3 4x dx= (1/6). (ii). ∫_0 ^( (𝛑/6)) cos^4 3𝛉 sin^2 6𝛉 d𝛉 = ((5𝛑)/(192)).

Question Number 90570 Answers: 1 Comments: 1

find the sum of Σ_(n=1) ^∞ (((−1)^n )/((2n+1)3^n ))

$${find}\:{the}\:{sum}\:{of}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)\mathrm{3}^{{n}} } \\ $$

Question Number 90566 Answers: 0 Comments: 0

∫_0 ^(infinity) Sin^4 3x/x^2 dx

$$\int_{\mathrm{0}} ^{\mathrm{infinity}} \mathrm{Sin}^{\mathrm{4}} \mathrm{3x}/\mathrm{x}^{\mathrm{2}} \mathrm{dx} \\ $$

Question Number 90564 Answers: 0 Comments: 1

find lim_(x→0) (((^3 (√(1+cos(2x)))−(^3 (√2)))/(x^2 sin(3x)))

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\frac{\left(^{\mathrm{3}} \sqrt{\mathrm{1}+{cos}\left(\mathrm{2}{x}\right)}−\left(^{\mathrm{3}} \sqrt{\mathrm{2}}\right)\right.}{{x}^{\mathrm{2}} {sin}\left(\mathrm{3}{x}\right)} \\ $$

Question Number 90562 Answers: 0 Comments: 2

prove that Σ_(n=1) ^∞ (1/(2n(2n−1)))=ln2

$${prove}\:{that} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}{n}\left(\mathrm{2}{n}−\mathrm{1}\right)}={ln}\mathrm{2} \\ $$

Question Number 90561 Answers: 0 Comments: 2

prove that Π_(n=2) ^∞ (1−(1/n^2 ))=(1/2)

$${prove}\:{that} \\ $$$$\underset{{n}=\mathrm{2}} {\overset{\infty} {\prod}}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 90557 Answers: 0 Comments: 7

Find the area enclose by the line y = x − 1 and the parabola y^2 = 2x + 6

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{enclose}\:\mathrm{by}\:\mathrm{the}\:\mathrm{line}\:\:\:\mathrm{y}\:\:=\:\:\mathrm{x}\:\:−\:\:\mathrm{1}\:\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{parabola}\:\:\:\mathrm{y}^{\mathrm{2}} \:\:=\:\:\mathrm{2x}\:\:+\:\:\mathrm{6} \\ $$

Question Number 90555 Answers: 1 Comments: 2

Question Number 90581 Answers: 1 Comments: 0

given that α and β are roots of the equation aχ^2 +bχ+c=0. show that λμb^2 =ac(λ+μ)^(2 ) where (α/β)=(λ/μ)

$${given}\:{that}\:\alpha\:{and}\:\beta\:{are}\:{roots}\:{of}\:\:{the}\:{equation}\: \\ $$$${a}\chi^{\mathrm{2}} +{b}\chi+{c}=\mathrm{0}.\:{show}\:{that}\:\lambda\mu{b}^{\mathrm{2}} ={ac}\left(\lambda+\mu\right)^{\mathrm{2}\:} \\ $$$${where}\:\frac{\alpha}{\beta}=\frac{\lambda}{\mu} \\ $$

Question Number 90550 Answers: 0 Comments: 3

x^4 + (1/x^4 ) = 527 (x−1)(x−2)(x−3)(x−4) ?

$${x}^{\mathrm{4}} \:+\:\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\:=\:\mathrm{527}\: \\ $$$$\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\left({x}−\mathrm{3}\right)\left({x}−\mathrm{4}\right)\:?\: \\ $$

Question Number 90544 Answers: 1 Comments: 0

∫ (dx/(√(2−cos x)))

$$\int\:\frac{{dx}}{\sqrt{\mathrm{2}−\mathrm{cos}\:{x}}} \\ $$

Question Number 90535 Answers: 1 Comments: 0

In a triangle ABC, a(b cos C−c cos B)=

$$\mathrm{In}\:\mathrm{a}\:\mathrm{triangle}\:{ABC},\:{a}\left({b}\:\mathrm{cos}\:{C}−{c}\:\mathrm{cos}\:{B}\right)= \\ $$

Question Number 90531 Answers: 0 Comments: 2

Please help me to find the value of ′n′ C_8 ^(n+3) =C_(20) ^(n+3)

$${Please}\:{help}\:{me}\:{to}\:{find}\:{the}\:{value} \\ $$$${of}\:\:\:'{n}' \\ $$$${C}_{\mathrm{8}} ^{{n}+\mathrm{3}} ={C}_{\mathrm{20}} ^{{n}+\mathrm{3}} \\ $$

Question Number 90520 Answers: 2 Comments: 1

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