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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 ))

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

Question Number 93477 Answers: 2 Comments: 0

Differentiate completely; 1\ f(x,y)=x^2 +xy^2 +siny 2\ f(x,y)=e^(x^2 +y^2 ) 3\ f(x,y,z)=tan(3x−y)+6^(y+2)

$$\mathrm{Differentiate}\:\mathrm{completely}; \\ $$$$\mathrm{1}\backslash\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}^{\mathrm{2}} +\mathrm{xy}^{\mathrm{2}} +\mathrm{siny} \\ $$$$\mathrm{2}\backslash\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{e}^{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} } \\ $$$$\mathrm{3}\backslash\:\mathrm{f}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\mathrm{tan}\left(\mathrm{3x}−\mathrm{y}\right)+\mathrm{6}^{\mathrm{y}+\mathrm{2}} \\ $$

Question Number 93474 Answers: 2 Comments: 0

Q. Prove by mathematical induction that Σ_(r=1) ^n (4r + 5) = 2n^2 + 7n

$$\mathrm{Q}.\:\mathrm{Prove}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}\:\mathrm{that}\: \\ $$$$\:\:\:\:\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\:\left(\mathrm{4}{r}\:+\:\mathrm{5}\right)\:=\:\mathrm{2}{n}^{\mathrm{2}} \:+\:\mathrm{7}{n}\: \\ $$

Question Number 93473 Answers: 1 Comments: 1

∫1/(1+x^2 )^2

$$\int\mathrm{1}/\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} \\ $$

Question Number 93471 Answers: 1 Comments: 0

∫1/1+x2

$$\int\mathrm{1}/\mathrm{1}+\mathrm{x2} \\ $$

Question Number 93470 Answers: 1 Comments: 4

Solve: 3x^(x + 1) − 3x^(x − 1) = 8

$$\boldsymbol{\mathrm{Solve}}:\:\:\:\:\mathrm{3}\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}\:\:+\:\:\mathrm{1}} \:\:−\:\:\mathrm{3}\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}\:\:−\:\:\mathrm{1}} \:\:\:=\:\:\:\:\mathrm{8} \\ $$

Question Number 93467 Answers: 1 Comments: 0

∫ (sin x+2cos x)^3 dx

$$\int\:\left(\mathrm{sin}\:\mathrm{x}+\mathrm{2cos}\:\mathrm{x}\right)^{\mathrm{3}} \:\mathrm{dx}\: \\ $$

Question Number 93464 Answers: 1 Comments: 0

If f a function such that f(a).f(b)−f(a+b)=a+b. find the value of f(2019)

$$\mathrm{If}\:\mathrm{f}\:\mathrm{a}\:\mathrm{function}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{f}\left(\mathrm{a}\right).\mathrm{f}\left(\mathrm{b}\right)−\mathrm{f}\left(\mathrm{a}+\mathrm{b}\right)=\mathrm{a}+\mathrm{b}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{2019}\right)\: \\ $$

Question Number 93460 Answers: 1 Comments: 1

solve for x,y >0 2x⌊y⌋ = 2020 3y⌊x⌋ = 2021

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x},\mathrm{y}\:>\mathrm{0} \\ $$$$\mathrm{2}{x}\lfloor\mathrm{y}\rfloor\:=\:\mathrm{2020} \\ $$$$\mathrm{3y}\lfloor{x}\rfloor\:=\:\mathrm{2021}\: \\ $$

Question Number 93451 Answers: 0 Comments: 3

Solve by using change the conistant megbod 4y^(′′) +y=((x^2 −1)/(x(√x)))?

$${Solve}\:{by}\:{using}\:{change}\:{the}\:{conistant}\:{megbod}\: \\ $$$$\mathrm{4}{y}^{''} +{y}=\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}\sqrt{{x}}}? \\ $$

Question Number 93450 Answers: 2 Comments: 0

what is the value of coefficient of x^9 in expansion (1+x)(1+x^2 ) (1+x^3 )(1+x^4 )×...×(1+x^(100) ) ?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{coefficient} \\ $$$$\mathrm{of}\:\mathrm{x}^{\mathrm{9}} \:\mathrm{in}\:\mathrm{expansion}\:\left(\mathrm{1}+\mathrm{x}\right)\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right) \\ $$$$\left(\mathrm{1}+\mathrm{x}^{\mathrm{3}} \right)\left(\mathrm{1}+\mathrm{x}^{\mathrm{4}} \right)×...×\left(\mathrm{1}+\mathrm{x}^{\mathrm{100}} \right)\:? \\ $$

Question Number 93442 Answers: 0 Comments: 3

To tinkutara I have forget my old password and has to create a new one. Is there any way to retrive my old account.

$$\mathrm{To}\:\mathrm{tinkutara} \\ $$$$\mathrm{I}\:\mathrm{have}\:\mathrm{forget}\:\mathrm{my}\:\mathrm{old}\:\mathrm{password}\:\mathrm{and}\:\mathrm{has}\:\mathrm{to}\:\mathrm{create}\:\mathrm{a} \\ $$$$\mathrm{new}\:\mathrm{one}.\:\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{way}\:\mathrm{to}\:\mathrm{retrive}\:\mathrm{my}\:\mathrm{old}\:\mathrm{account}. \\ $$

Question Number 93446 Answers: 0 Comments: 1

what is the coefficient of x^5 in the expansion (1+x^2 )(1+x)^4

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{5}} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{4}} \\ $$

Question Number 93439 Answers: 2 Comments: 0

Question Number 93434 Answers: 1 Comments: 1

Question Number 93428 Answers: 1 Comments: 0

Question Number 93418 Answers: 0 Comments: 3

let A= (((1 2 3)),((3 2 1)) ) ∈M_3 (C) (1 4 2 ) 1) find A^(−1) if A inversible 2) calculate A^n 3)find cosA and sinA 4) is cos^2 A +sin^2 A =I ?

$${let}\:{A}=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{2}\:\:\:\:\:\:\mathrm{3}}\\{\mathrm{3}\:\:\:\:\:\:\:\:\:\mathrm{2}\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix}\:\:\:\:\:\in{M}_{\mathrm{3}} \left({C}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{4}\:\:\:\:\:\:\:\mathrm{2}\:\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{A}^{−\mathrm{1}} \:{if}\:{A}\:{inversible} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{A}^{{n}} \\ $$$$\left.\mathrm{3}\right){find}\:{cosA}\:\:{and}\:{sinA} \\ $$$$\left.\mathrm{4}\right)\:{is}\:{cos}^{\mathrm{2}} \:{A}\:+{sin}^{\mathrm{2}} \:{A}\:={I}\:? \\ $$$$ \\ $$

Question Number 93415 Answers: 0 Comments: 5

let A = (((1 −1)),((1 1)) ) 1) calculate A^(−1) and A^(−2) 2) calculate A^n 3) find e^A and e^(−A)

$${let}\:\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:−\mathrm{1}}\\{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{−\mathrm{1}} \:{and}\:{A}^{−\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{A}^{{n}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{e}^{{A}} \:{and}\:{e}^{−{A}} \\ $$

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