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Question Number 93620    Answers: 1   Comments: 0

(3x+3y−4) (dy/dx) = x+y

$$\left(\mathrm{3x}+\mathrm{3y}−\mathrm{4}\right)\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{x}+\mathrm{y}\: \\ $$

Question Number 93618    Answers: 0   Comments: 1

Question Number 93610    Answers: 1   Comments: 0

∫(((√(x^n +1))/x))dx

$$\int\left(\frac{\sqrt{\mathrm{x}^{\mathrm{n}} +\mathrm{1}}}{\mathrm{x}}\right)\mathrm{dx} \\ $$

Question Number 93587    Answers: 3   Comments: 0

∫((x+1)/(x^2 −((1+(√5))/2)x+1))dx

$$\int\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}} −\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}}{dx} \\ $$

Question Number 93705    Answers: 0   Comments: 3

find real q so that x^4 −40x^2 +q = 0 has four real solution forming AP.

$$\mathrm{find}\:\mathrm{real}\:\mathrm{q}\:\mathrm{so}\:\mathrm{that}\:\mathrm{x}^{\mathrm{4}} −\mathrm{40x}^{\mathrm{2}} +\mathrm{q}\:=\:\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{four}\:\mathrm{real}\:\mathrm{solution}\:\mathrm{forming} \\ $$$$\mathrm{AP}.\: \\ $$

Question Number 93571    Answers: 0   Comments: 1

Prove that ((1−tan^3 θ)/(1+tan^3 θ)) =1−2sin^2 θ

$${Prove}\:{that}\:\frac{\mathrm{1}−{tan}^{\mathrm{3}} \theta}{\mathrm{1}+{tan}^{\mathrm{3}} \theta}\:=\mathrm{1}−\mathrm{2}{sin}^{\mathrm{2}} \theta \\ $$

Question Number 93569    Answers: 0   Comments: 0

Question Number 93568    Answers: 0   Comments: 1

Question Number 93567    Answers: 1   Comments: 1

Given that A={0,1,3,5} B={1,2,4,7} and C={1,2,3,5,8} prove that (i) (A∩B)∩C = A∩(B∩C) (ii) (A∪B)∪C = A∪(B∪C) (iii) (A∪B)∩C = (A∪C)∪(B∩C) (iv) (A∩C)∪B = (A∪B)∩(C∪B)

$${Given}\:{that}\:{A}=\left\{\mathrm{0},\mathrm{1},\mathrm{3},\mathrm{5}\right\}\:{B}=\left\{\mathrm{1},\mathrm{2},\mathrm{4},\mathrm{7}\right\}\:{and}\:{C}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{8}\right\}\:{prove}\:{that} \\ $$$$\left(\mathrm{i}\right)\:\left(\mathrm{A}\cap\mathrm{B}\right)\cap\mathrm{C}\:=\:\mathrm{A}\cap\left(\mathrm{B}\cap\mathrm{C}\right) \\ $$$$\left(\mathrm{ii}\right)\:\left(\mathrm{A}\cup\mathrm{B}\right)\cup\mathrm{C}\:=\:\mathrm{A}\cup\left(\mathrm{B}\cup\mathrm{C}\right) \\ $$$$\left(\mathrm{iii}\right)\:\left(\mathrm{A}\cup\mathrm{B}\right)\cap\mathrm{C}\:=\:\left(\mathrm{A}\cup\mathrm{C}\right)\cup\left(\mathrm{B}\cap\mathrm{C}\right) \\ $$$$\left(\mathrm{iv}\right)\:\left(\mathrm{A}\cap\mathrm{C}\right)\cup\mathrm{B}\:=\:\left(\mathrm{A}\cup\mathrm{B}\right)\cap\left(\mathrm{C}\cup\mathrm{B}\right) \\ $$

Question Number 93555    Answers: 0   Comments: 3

Question Number 93553    Answers: 0   Comments: 2

∫ln(1+e^u )du

$$\int{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{u}} \right)\mathrm{du} \\ $$

Question Number 93546    Answers: 0   Comments: 13

Which app is the best to evaluate ((W(2 ln 2))/(ln 2))

$$\:\:\mathrm{Which}\:\mathrm{app}\:\mathrm{is}\:\mathrm{the}\:\mathrm{best}\:\mathrm{to}\:\mathrm{evaluate} \\ $$$$\:\:\:\:\frac{\mathrm{W}\left(\mathrm{2}\:\mathrm{ln}\:\mathrm{2}\right)}{\mathrm{ln}\:\mathrm{2}} \\ $$

Question Number 93540    Answers: 0   Comments: 7

Question Number 93720    Answers: 0   Comments: 2

∫ (dx/((x+1)^3 (√(x^2 +2x))))

$$\int\:\frac{\boldsymbol{{dx}}}{\left(\boldsymbol{{x}}+\mathrm{1}\right)^{\mathrm{3}} \:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{2}\boldsymbol{{x}}}}\: \\ $$

Question Number 93534    Answers: 1   Comments: 0

A^2 = ((7,3),(9,4) ) ⇒ A = ((a,b),(c,d) ) Find the all of different matrices A (i) . If a, b, c, d ∈ Z (ii) . If a, b, c, d ∈ R^+

$${A}^{\mathrm{2}} \:\:=\:\:\begin{pmatrix}{\mathrm{7}}&{\mathrm{3}}\\{\mathrm{9}}&{\mathrm{4}}\end{pmatrix}\:\:\:\Rightarrow\:\:{A}\:=\:\begin{pmatrix}{{a}}&{{b}}\\{{c}}&{{d}}\end{pmatrix} \\ $$$${Find}\:\:{the}\:\:{all}\:\:{of}\:\:\:{different}\:\:{matrices}\:\:{A}\:\: \\ $$$$\left({i}\right)\:.\:{If}\:\:{a},\:{b},\:{c},\:{d}\:\in\:\mathbb{Z}\:\:\: \\ $$$$\left({ii}\right)\:.\:{If}\:\:{a},\:{b},\:{c},\:{d}\:\in\:\mathbb{R}^{+} \: \\ $$

Question Number 93530    Answers: 0   Comments: 4

(4x^2 +xy+y^2 )dx+(4y^2 +3xy+x^2 )dy=0

$$\left(\mathrm{4}{x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} \right){dx}+\left(\mathrm{4}{y}^{\mathrm{2}} +\mathrm{3}{xy}+{x}^{\mathrm{2}} \right){dy}=\mathrm{0} \\ $$

Question Number 93513    Answers: 1   Comments: 0

y^(′′) +y^′ −2y=0

$${y}^{''} +{y}^{'} −\mathrm{2}{y}=\mathrm{0} \\ $$

Question Number 93509    Answers: 0   Comments: 5

Σ_(n=1) ^∞ (1/(n^2 +5n+6))

$$\sum_{{n}=\mathrm{1}} ^{\infty} \frac{\mathrm{1}}{{n}^{\mathrm{2}} +\mathrm{5}{n}+\mathrm{6}}\: \\ $$

Question Number 93505    Answers: 0   Comments: 0

Does (x,y)+(x^′ ,y^′ )=(x+x^′ , y+y^′ ) form a vector space? λ(x,y)=(λx,λy)

$$\mathrm{Does} \\ $$$$\left(\mathrm{x},\mathrm{y}\right)+\left(\mathrm{x}^{'} ,\mathrm{y}^{'} \right)=\left(\mathrm{x}+\mathrm{x}^{'} ,\:\mathrm{y}+\mathrm{y}^{'} \right) \\ $$$$\mathrm{form}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{space}? \\ $$$$\lambda\left(\mathrm{x},\mathrm{y}\right)=\left(\lambda\mathrm{x},\lambda\mathrm{y}\right) \\ $$

Question Number 93512    Answers: 0   Comments: 2

(xy+sin y)dx+(0.5x^2 +xcos y)dy=o

$$\left({xy}+\mathrm{sin}\:{y}\right){dx}+\left(\mathrm{0}.\mathrm{5}{x}^{\mathrm{2}} +{x}\mathrm{cos}\:{y}\right){dy}={o} \\ $$

Question Number 93510    Answers: 0   Comments: 1

y^′ −y.tan x+y^2 cos x=0

$${y}^{'} −{y}.\mathrm{tan}\:{x}+{y}^{\mathrm{2}} \mathrm{cos}\:{x}=\mathrm{0} \\ $$

Question Number 93493    Answers: 0   Comments: 4

Question Number 93484    Answers: 0   Comments: 2

∫t^2 /(1+t^2 )^2 dx=

$$\int\mathrm{t}^{\mathrm{2}} /\left(\mathrm{1}+\mathrm{t}^{\mathrm{2}} \right)^{\mathrm{2}} \mathrm{dx}= \\ $$

Question Number 93483    Answers: 0   Comments: 0

prove that the equation of the normal to the rectangular hyperbola xy = c^2 at the point P(ct, c/t) is t^3 x −ty = c(t^4 −1). the normal to P on the hyperbola meets the x−axis at Q and the tangent to P meets the yaxis at R. show that the locus of the midpoint oc QR, as P varies is 2c^2 xy + y^4 = c^4 .

$$\:\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{normal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{rectangular} \\ $$$$\mathrm{hyperbola}\:{xy}\:=\:{c}^{\mathrm{2}} \:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:{P}\left({ct},\:{c}/{t}\right)\:\mathrm{is}\:{t}^{\mathrm{3}} {x}\:−{ty}\:=\:{c}\left({t}^{\mathrm{4}} −\mathrm{1}\right). \\ $$$$\mathrm{the}\:\mathrm{normal}\:\mathrm{to}\:{P}\:\:\mathrm{on}\:\mathrm{the}\:\mathrm{hyperbola}\:\mathrm{meets}\:\mathrm{the}\:\mathrm{x}−\mathrm{axis}\:\mathrm{at}\:{Q}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{tangent}\:\mathrm{to}\:{P}\:\mathrm{meets}\:\mathrm{the}\:\mathrm{yaxis}\:\mathrm{at}\:{R}.\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{the}\:\mathrm{midpoint}\:\:\mathrm{oc}\:{QR},\:\mathrm{as}\:{P}\:\mathrm{varies}\:\mathrm{is}\:\mathrm{2}{c}^{\mathrm{2}} {xy}\:+\:{y}^{\mathrm{4}} \:=\:{c}^{\mathrm{4}} . \\ $$

Question Number 93481    Answers: 1   Comments: 1

∫(log x/x^2 )dx=

$$\int\left(\mathrm{log}\:\mathrm{x}/\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx}= \\ $$

Question Number 93478    Answers: 0   Comments: 2

1\Calculate f_x (2,3) if f(x,y)=x^2 +y^2 2\Calculate df(x,y) for x=1, y=0, dx=(1/2) and dy=(1/4) if f(x,y)=(√(x^2 +y^2 ))

$$\mathrm{1}\backslash\mathrm{Calculate}\:\mathrm{f}_{\mathrm{x}} \left(\mathrm{2},\mathrm{3}\right)\:\mathrm{if}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{2}\backslash\mathrm{Calculate}\:\mathrm{df}\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{for}\:\mathrm{x}=\mathrm{1},\:\mathrm{y}=\mathrm{0},\:\mathrm{dx}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{and}\:\mathrm{dy}=\frac{\mathrm{1}}{\mathrm{4}}\:\mathrm{if}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} } \\ $$

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