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Question Number 91933 Answers: 1 Comments: 2

Question Number 91936 Answers: 0 Comments: 6

how to evaluate ln(i), i=(√(−1)).

$${how}\:{to}\:{evaluate}\:{ln}\left({i}\right),\:{i}=\sqrt{−\mathrm{1}}. \\ $$

Question Number 91931 Answers: 0 Comments: 3

∫_0 ^1 ln(Γ(x)) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\Gamma\left({x}\right)\right)\:{dx} \\ $$

Question Number 91930 Answers: 0 Comments: 2

lim_(x→0) cos (1/x)=

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}cos}\:\frac{\mathrm{1}}{{x}}= \\ $$

Question Number 91919 Answers: 0 Comments: 1

The value of sin 12° sin 48° sin 54° is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{sin}\:\mathrm{12}°\:\mathrm{sin}\:\mathrm{48}°\:\mathrm{sin}\:\mathrm{54}°\:\:\mathrm{is} \\ $$

Question Number 91914 Answers: 1 Comments: 0

hi every one here i will put my solution for old question by mr.MJS ∫((√((x−1)x(x+1)))/(3x^2 −4))dx the solution by using Appell hypergeometric function

$${hi}\:{every}\:{one}\:{here}\:{i}\:{will}\:{put}\:{my}\:{solution}\:\: \\ $$$${for}\:{old}\:{question}\:{by}\:{mr}.{MJS} \\ $$$$\int\frac{\sqrt{\left({x}−\mathrm{1}\right){x}\left({x}+\mathrm{1}\right)}}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}}{dx} \\ $$$$ \\ $$$${the}\:{solution}\:{by}\:{using}\:\:\: \\ $$$${Appell}\:{hypergeometric}\:{function} \\ $$

Question Number 91912 Answers: 0 Comments: 2

if ∣x∣, ∣x−1∣, ∣x+1∣ are first three terms of an AP. then what is the sum of it′s first 10 terms equal to

$$\mathrm{if}\:\mid\mathrm{x}\mid,\:\mid\mathrm{x}−\mathrm{1}\mid,\:\mid\mathrm{x}+\mathrm{1}\mid\:\mathrm{are}\:\mathrm{first} \\ $$$$\mathrm{three}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{AP}.\:\mathrm{then}\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{it}'\mathrm{s}\:\mathrm{first} \\ $$$$\mathrm{10}\:\mathrm{terms}\:\mathrm{equal}\:\mathrm{to}\: \\ $$

Question Number 91911 Answers: 1 Comments: 0

y′′′′+2y′′+y=sin x

$$\mathrm{y}''''+\mathrm{2y}''+\mathrm{y}=\mathrm{sin}\:\mathrm{x}\: \\ $$

Question Number 91910 Answers: 1 Comments: 5

∫((ln(1+sin^2 x))/(sin^2 x))dx

$$\int\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \mathrm{x}\right)}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\mathrm{dx} \\ $$

Question Number 91904 Answers: 1 Comments: 3

∫_1 ^e^π ((cos(lnx))/x)dx

$$\int_{\mathrm{1}} ^{\mathrm{e}^{\pi} } \frac{\mathrm{cos}\left(\mathrm{lnx}\right)}{\mathrm{x}}\mathrm{dx} \\ $$

Question Number 91897 Answers: 0 Comments: 1

lim_(x→0) ((sin (2x−sin x))/(1−(√(1−x^2 )))) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{2}{x}−\mathrm{sin}\:{x}\right)}{\mathrm{1}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:=\:? \\ $$

Question Number 91892 Answers: 0 Comments: 5

∫_0 ^π (dx/(a^2 cos^2 x+b^2 sin^2 x)) ?

$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{{dx}}{{a}^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} {x}+{b}^{\mathrm{2}} \:\mathrm{sin}\:^{\mathrm{2}} {x}}\:? \\ $$

Question Number 91872 Answers: 0 Comments: 3

solve in R 8(√(x^4 +1))+5(√(x^3 +1))=7x^2 +12

$${solve}\:{in}\:\mathbb{R} \\ $$$$\mathrm{8}\sqrt{\mathrm{x}^{\mathrm{4}} +\mathrm{1}}+\mathrm{5}\sqrt{\mathrm{x}^{\mathrm{3}} +\mathrm{1}}=\mathrm{7x}^{\mathrm{2}} +\mathrm{12} \\ $$

Question Number 91870 Answers: 0 Comments: 5

(1^ /x^(2x) ) + x^(−4x) = 6, (x ≠ 0) x = ?_

$$\:\frac{\overset{\:} {\mathrm{1}}}{\mathrm{x}^{\mathrm{2x}} }\:+\:\mathrm{x}^{−\mathrm{4x}} \:=\:\mathrm{6},\:\:\left(\mathrm{x}\:\neq\:\mathrm{0}\right) \\ $$$$\: \\ $$$$\:\mathrm{x}\:=\:\underset{\:} {?} \\ $$

Question Number 91862 Answers: 1 Comments: 4

log_2 (x)+log_3 (x) = 1 x =?

$$\mathrm{log}_{\mathrm{2}} \left({x}\right)+\mathrm{log}_{\mathrm{3}} \left({x}\right)\:=\:\mathrm{1} \\ $$$${x}\:=? \\ $$

Question Number 91850 Answers: 0 Comments: 3

Question Number 91848 Answers: 0 Comments: 1

y^(′′) −4y^′ +4y=(x+1)e^(2x)

$${y}^{''} −\mathrm{4}{y}^{'} +\mathrm{4}{y}=\left({x}+\mathrm{1}\right){e}^{\mathrm{2}{x}} \\ $$$$ \\ $$

Question Number 91844 Answers: 0 Comments: 5

Question Number 91843 Answers: 2 Comments: 5

{ (((1/x)+y = 2)),((x+(1/y) = 3)) :} find x^2 +y^2

$$\begin{cases}{\frac{\mathrm{1}}{{x}}+{y}\:=\:\mathrm{2}}\\{{x}+\frac{\mathrm{1}}{{y}}\:=\:\mathrm{3}}\end{cases} \\ $$$${find}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$

Question Number 91842 Answers: 1 Comments: 1

∫ (dx/(x(√(4x^2 +2x−1)))) ?

$$\int\:\frac{{dx}}{{x}\sqrt{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}}}\:? \\ $$

Question Number 91840 Answers: 0 Comments: 0

solve y y′′=(y′)^2 +y′(√(y^2 +(y′)^2 ))

$${solve}\: \\ $$$${y}\:{y}''=\left({y}'\right)^{\mathrm{2}} +{y}'\sqrt{{y}^{\mathrm{2}} +\left({y}'\right)^{\mathrm{2}} } \\ $$

Question Number 91837 Answers: 0 Comments: 5

1). Σ_(n=1) ^∞ ((5/(n+2))−(5/(n+3)) )=... 2). Σ_(n=1) ^∞ ((1/(4n^2 −1)))=... 3). Σ_(n=1) ^∞ (((3n)/(5n−1)) )=... Σ_(n=1) ^∞ ((n/(n+1)) )=...

$$\left.\mathrm{1}\right).\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{5}}{\mathrm{n}+\mathrm{2}}−\frac{\mathrm{5}}{\mathrm{n}+\mathrm{3}}\:\right)=... \\ $$$$ \\ $$$$\left.\mathrm{2}\right).\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{4n}^{\mathrm{2}} −\mathrm{1}}\right)=... \\ $$$$ \\ $$$$\left.\mathrm{3}\right).\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{3n}}{\mathrm{5n}−\mathrm{1}}\:\right)=... \\ $$$$ \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{n}}{\mathrm{n}+\mathrm{1}}\:\right)=... \\ $$

Question Number 91836 Answers: 1 Comments: 1

Question Number 91825 Answers: 2 Comments: 3

(cos x) (dy/dx)−y(sin x) = cot (x)

$$\left(\mathrm{cos}\:{x}\right)\:\frac{{dy}}{{dx}}−{y}\left(\mathrm{sin}\:{x}\right)\:=\:\mathrm{cot}\:\left({x}\right) \\ $$

Question Number 92524 Answers: 0 Comments: 0

(d^3 x/dt^3 ) + 27 (d^2 x/dt^2 ) + 243 (dx/dt) + 729x = t∙ e^(−9t) x(0) = x′(0) = x^(′′) (0) = 0 Use Laplace Transformation to solve it .

$$\frac{{d}^{\mathrm{3}} {x}}{{dt}^{\mathrm{3}} }\:+\:\mathrm{27}\:\frac{{d}^{\mathrm{2}} {x}}{{dt}^{\mathrm{2}} }\:+\:\mathrm{243}\:\frac{{dx}}{{dt}}\:+\:\mathrm{729}{x}\:=\:{t}\centerdot\:{e}^{−\mathrm{9}{t}} \\ $$$$\:\:\:\:\:\:{x}\left(\mathrm{0}\right)\:=\:{x}'\left(\mathrm{0}\right)\:=\:{x}^{''} \left(\mathrm{0}\right)\:=\:\mathrm{0} \\ $$$${Use}\:\:{Laplace}\:\:{Transformation}\:\:{to}\:\:{solve}\:\:{it}\:. \\ $$

Question Number 91813 Answers: 0 Comments: 3

lim_(x→1) ((1−x+ ln x)/(1−(√(2x−x^2 )))) ?

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{1}−{x}+\:\mathrm{ln}\:{x}}{\mathrm{1}−\sqrt{\mathrm{2}{x}−{x}^{\mathrm{2}} }}\:? \\ $$

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