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Question Number 83721 Answers: 3 Comments: 8

Question Number 83719 Answers: 2 Comments: 1

Question. ^(Show that ∫_0 ^(Π/2) ((cosx)/(3+cos^2 x))dx=(1/4)ln3)

$${Question}.\:\:\:\:\:\:\:\:\overset{{Show}\:\:{that}\:\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} \frac{{cosx}}{\mathrm{3}+{cos}^{\mathrm{2}} {x}}{dx}=\frac{\mathrm{1}}{\mathrm{4}}{ln}\mathrm{3}} {\:} \\ $$

Question Number 83717 Answers: 0 Comments: 0

Question Number 83713 Answers: 1 Comments: 8

∫(dx/(√(x+(√(x+(√x)))))) pleas sir help me

$$\int\frac{{dx}}{\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}}\:\:\:{pleas}\:{sir}\:{help}\:{me} \\ $$

Question Number 83710 Answers: 0 Comments: 1

lim_(x→∞) (((1+(√5))^x −(1−(√5))^x )/((1+(√5))^(x−1) −(1−(√5))^(x−1) )) = ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)^{{x}} −\left(\mathrm{1}−\sqrt{\mathrm{5}}\right)^{{x}} }{\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)^{{x}−\mathrm{1}} −\left(\mathrm{1}−\sqrt{\mathrm{5}}\right)^{{x}−\mathrm{1}} }\:=\:? \\ $$

Question Number 83706 Answers: 1 Comments: 0

4^x + 10^x = 25^x x = ?

$$\mathrm{4}^{\mathrm{x}} \:+\:\mathrm{10}^{\mathrm{x}} \:=\:\mathrm{25}^{\mathrm{x}} \\ $$$$\mathrm{x}\:=\:? \\ $$

Question Number 83694 Answers: 2 Comments: 2

Question Number 83691 Answers: 1 Comments: 2

evaluate: ∫ (( dx)/(a sin x+b cos x))

$$\:\mathrm{evaluate}: \\ $$$$\:\:\:\int\:\frac{\:\boldsymbol{\mathrm{dx}}}{\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{b}}\:\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}} \\ $$

Question Number 83690 Answers: 1 Comments: 1

lim_(x→∞ ) ((tan (((πx+1)/(2x+2))))/(x+1)) = ?

$$\underset{{x}\rightarrow\infty\:} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\frac{\pi{x}+\mathrm{1}}{\mathrm{2}{x}+\mathrm{2}}\right)}{{x}+\mathrm{1}}\:=\:? \\ $$

Question Number 83680 Answers: 0 Comments: 4

Question Number 83675 Answers: 1 Comments: 2

evaluate: 2 ∫_0 ^( 2) ((√(x+1))/(x^2 +4))dx

$$ \\ $$$$\: \\ $$$$\:\:\mathrm{evaluate}: \\ $$$$\:\mathrm{2}\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \:\frac{\sqrt{\mathrm{x}+\mathrm{1}}}{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}\mathrm{dx} \\ $$$$\:\:\:\:\: \\ $$$$\:\: \\ $$

Question Number 83674 Answers: 1 Comments: 1

Question Number 83672 Answers: 2 Comments: 0

x^2 + (1/x^2 ) = 51 find x

$${x}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:=\:\mathrm{51}\: \\ $$$${find}\:{x}\: \\ $$

Question Number 83668 Answers: 1 Comments: 0

lim_(x→0) ((sin x cos x−x)/(x^2 sin (2x))) =

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}−{x}}{{x}^{\mathrm{2}} \:\mathrm{sin}\:\left(\mathrm{2}{x}\right)}\:=\: \\ $$

Question Number 83662 Answers: 1 Comments: 3

if f(x) = (√(x^2 −1)) and g(x) = (1/(√(x^2 −3))) find domain function (g • f)(x)

$$\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\:\:\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{3}}} \\ $$$$\mathrm{find}\:\mathrm{domain}\:\mathrm{function}\: \\ $$$$\left(\mathrm{g}\:\bullet\:\mathrm{f}\right)\left(\mathrm{x}\right) \\ $$

Question Number 83654 Answers: 2 Comments: 1

solve this equation sin^2 x−sin^4 x=cos^2 x−cos^4 x

$$\mathrm{solve}\:\mathrm{this}\:\mathrm{equation}\: \\ $$$$\mathrm{sin}\:^{\mathrm{2}} {x}−\mathrm{sin}\:^{\mathrm{4}} {x}=\mathrm{cos}\:^{\mathrm{2}} {x}−\mathrm{cos}\:^{\mathrm{4}} {x} \\ $$

Question Number 83653 Answers: 2 Comments: 0

find range of function y= (4/((x^2 −4)))

$$\mathrm{find}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{y}=\:\frac{\mathrm{4}}{\left({x}^{\mathrm{2}} −\mathrm{4}\right)} \\ $$

Question Number 83649 Answers: 1 Comments: 0

Question Number 83644 Answers: 0 Comments: 0

Question Number 83642 Answers: 0 Comments: 0

Find the surface area of the solid generated by the revolution of the cardioids r=a(1+cos θ) about the initial line.

$$ \\ $$$$\: \\ $$$$\mathfrak{Find}\:\mathfrak{the}\:\mathfrak{surface}\:\mathfrak{area}\:\mathfrak{of}\:\mathfrak{the}\:\mathfrak{solid}\:\mathfrak{generated} \\ $$$$\:\:\mathfrak{by}\:\mathfrak{the}\:\mathfrak{revolution}\:\mathfrak{of}\:\mathfrak{the}\:\mathfrak{cardioids}\:\mathfrak{r}=\mathfrak{a}\left(\mathrm{1}+\mathfrak{cos}\:\theta\right)\:\mathfrak{about}\:\mathfrak{the}\:\mathfrak{initial}\:\mathfrak{line}. \\ $$

Question Number 83637 Answers: 0 Comments: 0

Question Number 83639 Answers: 4 Comments: 0

Find the differential equations: (i) log((dy/dx))=ax+by (ii) x cos y dy=(x e^x log x +e^x )dx

$$ \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equations}}: \\ $$$$\:\:\:\left(\mathrm{i}\right)\:\mathrm{log}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)=\mathrm{ax}+\mathrm{by} \\ $$$$\:\:\:\left(\mathrm{ii}\right)\:\mathrm{x}\:\mathrm{cos}\:\mathrm{y}\:\mathrm{dy}=\left(\mathrm{x}\:\mathrm{e}^{\mathrm{x}} \mathrm{log}\:\mathrm{x}\:+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$$$ \\ $$

Question Number 83638 Answers: 1 Comments: 0

Question Number 83629 Answers: 1 Comments: 0

show that Σ_(n,k=0) ^∞ ((n! k!)/((n+k+2)!))=(π^2 /6)

$${show}\:{that} \\ $$$$\underset{{n},{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{n}!\:{k}!}{\left({n}+{k}+\mathrm{2}\right)!}=\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$

Question Number 83619 Answers: 0 Comments: 0

Show that the differetial equation is a Sturm−Louville equation (x^(−1) y^1 )^1 +(4+λ)x^(−3) y=0, y(1)=0,y(ϱ^t )=0 Solve the equation to determine the eigenvalue and the corresponding eigen functions of the problem. Show also that the set of eigen function forms and orthogonal and orthonormal set. Thanks as usual.

$${Show}\:{that}\:{the}\:{differetial}\:{equation}\:{is}\:{a}\:{Sturm}−{Louville}\:{equation} \\ $$$$\left({x}^{−\mathrm{1}} {y}^{\mathrm{1}} \right)^{\mathrm{1}} +\left(\mathrm{4}+\lambda\right){x}^{−\mathrm{3}} {y}=\mathrm{0},\:\:{y}\left(\mathrm{1}\right)=\mathrm{0},{y}\left(\varrho^{{t}} \right)=\mathrm{0} \\ $$$${Solve}\:{the}\:{equation}\:{to}\:{determine}\:{the}\:{eigenvalue}\:{and}\:{the}\:{corresponding}\:{eigen}\:{functions}\:{of}\:{the}\:{problem}. \\ $$$${Show}\:{also}\:{that}\:{the}\:{set}\:{of}\:{eigen}\:{function}\:{forms}\:{and}\:{orthogonal}\:{and}\:{orthonormal}\:{set}. \\ $$$$ \\ $$$${Thanks}\:{as}\:{usual}. \\ $$

Question Number 83614 Answers: 1 Comments: 1

(3x−5)(3x+4)

$$\left(\mathrm{3}{x}−\mathrm{5}\right)\left(\mathrm{3}{x}+\mathrm{4}\right) \\ $$$$ \\ $$

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