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Question Number 183989 Answers: 4 Comments: 1

(((√x) + (√(x − 4a)))/( (√x) − (√(x − 4a)))) = a ≠ 0 find “x” in terms of “a”.

$$\frac{\sqrt{{x}}\:+\:\sqrt{{x}\:−\:\mathrm{4}{a}}}{\:\sqrt{{x}}\:−\:\sqrt{{x}\:−\:\mathrm{4}{a}}}\:=\:{a}\:\neq\:\mathrm{0} \\ $$$$\:{find}\:``{x}''\:{in}\:{terms}\:{of}\:``{a}''.\: \\ $$

Question Number 183977 Answers: 3 Comments: 0

∫_0 ^( ∞) (dx/(x^8 +x^4 +1)) =?

$$\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{dx}}{{x}^{\mathrm{8}} +{x}^{\mathrm{4}} +\mathrm{1}}\:=?\: \\ $$

Question Number 183976 Answers: 1 Comments: 0

∫ ((sin x−(√(1+sin x)))/(cos x−(√(1+cos x)))) dx =?

$$\:\:\int\:\frac{\mathrm{sin}\:{x}−\sqrt{\mathrm{1}+\mathrm{sin}\:{x}}}{\mathrm{cos}\:{x}−\sqrt{\mathrm{1}+\mathrm{cos}\:{x}}}\:{dx}\:=? \\ $$

Question Number 183974 Answers: 1 Comments: 0

Question Number 183967 Answers: 2 Comments: 0

Σ_(n=1) ^∞ (((−1)^(n+1) )/(3n−1)) = ?

$$\:\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}+\mathrm{1}} }{\mathrm{3}\boldsymbol{\mathrm{n}}−\mathrm{1}}\:\:=\:\:\:? \\ $$

Question Number 183965 Answers: 1 Comments: 0

A linear transformation E, of the x−y plane is defined as E:(x, y) → (2x+y, 2x+3y) Find the equation of the line that remains invariant under the transformation.

$$\mathrm{A}\:\mathrm{linear}\:\mathrm{transformation}\:\boldsymbol{{E}},\:\mathrm{of}\:\mathrm{the} \\ $$$${x}−{y}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{as} \\ $$$$\:\:\:\:\:\:\:\boldsymbol{{E}}:\left({x},\:{y}\right)\:\rightarrow\:\left(\mathrm{2}{x}+{y},\:\mathrm{2}{x}+\mathrm{3}{y}\right) \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mathrm{that} \\ $$$$\mathrm{remains}\:\mathrm{invariant}\:\mathrm{under}\:\mathrm{the} \\ $$$$\mathrm{transformation}. \\ $$

Question Number 183962 Answers: 2 Comments: 1

Question Number 183951 Answers: 2 Comments: 1

Question Number 183945 Answers: 2 Comments: 0

Question Number 183943 Answers: 0 Comments: 1

∫_(1−(√(πx))(d^(1/2) /dx^(1/2) )(1)) ^(Σ_(n=1) ^∞ (4/(4n^2 −1)) ) ((arctan(((2−x)/(1+2x))))/(x^2 −4x−1))dx

$$\int_{\mathrm{1}−\sqrt{\pi{x}}\frac{{d}^{\frac{\mathrm{1}}{\mathrm{2}}} }{{dx}^{\frac{\mathrm{1}}{\mathrm{2}}} }\left(\mathrm{1}\right)} ^{\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{4}}{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:} \frac{\mathrm{arctan}\left(\frac{\mathrm{2}−{x}}{\mathrm{1}+\mathrm{2}{x}}\right)}{{x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{1}}{dx} \\ $$

Question Number 183936 Answers: 1 Comments: 0

Question Number 183935 Answers: 3 Comments: 0

(√(x^2 +2))+(√(x^2 −4))=A (√(x^2 +2))−(√(x^2 −4))=?

$$\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}+\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}={A} \\ $$$$\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}=? \\ $$

Question Number 183927 Answers: 2 Comments: 0

lim_(x→2 ) ((tan (2πx)+cos ((π/2)x)+tan ((π/8)x))/(x^2 +4x−12)) =?

$$\:\underset{{x}\rightarrow\mathrm{2}\:} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\mathrm{2}\pi{x}\right)+\mathrm{cos}\:\left(\frac{\pi}{\mathrm{2}}{x}\right)+\mathrm{tan}\:\left(\frac{\pi}{\mathrm{8}}{x}\right)}{{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{12}}\:=? \\ $$

Question Number 183913 Answers: 0 Comments: 0

Question Number 183893 Answers: 0 Comments: 2

Question Number 183886 Answers: 4 Comments: 0

Question Number 183879 Answers: 0 Comments: 0

Question Number 183865 Answers: 1 Comments: 0

Question Number 183864 Answers: 4 Comments: 2

Question Number 183863 Answers: 1 Comments: 0

Question Number 183850 Answers: 0 Comments: 0

𝚺_(n=1) ^∞ (1/(n^3 (((6n)),((3n)) )))

$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}^{\mathrm{3}} \begin{pmatrix}{\mathrm{6}\boldsymbol{\mathrm{n}}}\\{\mathrm{3}\boldsymbol{\mathrm{n}}}\end{pmatrix}} \\ $$

Question Number 183848 Answers: 2 Comments: 1

Question Number 183847 Answers: 5 Comments: 0

Question Number 183846 Answers: 4 Comments: 0

Question Number 183845 Answers: 2 Comments: 0

Question Number 183844 Answers: 2 Comments: 0

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