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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)

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

Question Number 93414 Answers: 0 Comments: 0

let p(x)=((x^n (4−2x)^n )/(n!)) 1) prove that p^((k)) (0)=p^((k)) (2)=0 for all k∈[1,n−1] 2) prove that ∀m∈N p^((m)) (0) and p^((m)) (2) are integrs

$${let}\:{p}\left({x}\right)=\frac{{x}^{{n}} \left(\mathrm{4}−\mathrm{2}{x}\right)^{{n}} }{{n}!} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:{p}^{\left({k}\right)} \left(\mathrm{0}\right)={p}^{\left({k}\right)} \left(\mathrm{2}\right)=\mathrm{0}\:{for}\:{all}\:{k}\in\left[\mathrm{1},{n}−\mathrm{1}\right] \\ $$$$\left.\mathrm{2}\right)\:\:{prove}\:{that}\:\:\forall{m}\in{N}\:\:\:\:{p}^{\left({m}\right)} \left(\mathrm{0}\right)\:{and}\:{p}^{\left({m}\right)} \left(\mathrm{2}\right)\:{are}\:{integrs} \\ $$

Question Number 93410 Answers: 0 Comments: 7

∫((1+x^6 )/(1+x^8 ))dx

$$\int\frac{\mathrm{1}+{x}^{\mathrm{6}} }{\mathrm{1}+{x}^{\mathrm{8}} }{dx} \\ $$

Question Number 93397 Answers: 0 Comments: 2

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

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

Question Number 93388 Answers: 0 Comments: 2

Question Number 93376 Answers: 0 Comments: 1

x^x^x =((1/2))^(1/2) x=?

$$ \\ $$$${x}^{{x}^{{x}} } =\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$${x}=? \\ $$

Question Number 93371 Answers: 0 Comments: 21

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$$\mathrm{New}\:\mathrm{version}\:\mathrm{of}\:\mathrm{the}\:\mathrm{app}\:\mathrm{with}\:\mathrm{usability} \\ $$$$\mathrm{enhacements}\:\mathrm{is}\:\mathrm{now}\:\mathrm{available}\:\mathrm{on} \\ $$$$\mathrm{playstore}. \\ $$$$\mathrm{Pleasd}\:\mathrm{update}\:\mathrm{app}.\: \\ $$$$\mathrm{Comment}\:\mathrm{on}\:\mathrm{this}\:\mathrm{post}\:\mathrm{for} \\ $$$$\mathrm{problem}/\mathrm{feedback}\:\mathrm{suggestions}. \\ $$

Question Number 93368 Answers: 1 Comments: 0

given that f(r)= sin (1 + 2r)θ show that f(r)−f(r−1) = 2 cos 2r θ sin θ hence show that Σ_(r=1) ^n cos 2r θ sin θ = cos (n +1)θ sin nθ

$$\mathrm{given}\:\mathrm{that}\:{f}\left({r}\right)=\:\:\mathrm{sin}\:\left(\mathrm{1}\:+\:\mathrm{2}{r}\right)\theta \\ $$$$\mathrm{show}\:\mathrm{that}\:{f}\left({r}\right)−{f}\left({r}−\mathrm{1}\right)\:=\:\mathrm{2}\:\mathrm{cos}\:\mathrm{2}{r}\:\theta\:\mathrm{sin}\:\theta \\ $$$$\mathrm{hence}\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\:\:\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\:\mathrm{cos}\:\mathrm{2}{r}\:\theta\:\mathrm{sin}\:\theta\:\:=\:\mathrm{cos}\:\left({n}\:+\mathrm{1}\right)\theta\:\mathrm{sin}\:{n}\theta \\ $$

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