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Question Number 156107    Answers: 1   Comments: 1

(1+(1/x))^(x+1) =(1+(1/(2019)))^(2019)

$$\:\:\:\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}+\mathrm{1}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2019}}\right)^{\mathrm{2019}} \\ $$

Question Number 156106    Answers: 0   Comments: 0

Find an equation of the tangen line to the graph of the given equation at the indicated point P 1). xy+16=0 →P(−2,8) 2). y^2 −4x^2 =5→P(−1,3) 3). 2x^3 −x^2 y+y^3 −1=0→P(2,−3) 4). 3y^4 +4x−x^2 sin y−4=0→P(1,0) 5). y^4 +3 y−4x^2 =5x+1→P(1,−2)

$$\mathrm{Find}\:\mathrm{an}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tangen}\:\mathrm{line} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:\mathrm{the}\:\mathrm{given}\:\mathrm{equation}\: \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{indicated}\:\mathrm{point}\:\mathrm{P} \\ $$$$\left.\mathrm{1}\right).\:\:\mathrm{xy}+\mathrm{16}=\mathrm{0}\:\rightarrow\mathrm{P}\left(−\mathrm{2},\mathrm{8}\right) \\ $$$$\left.\mathrm{2}\right).\:\:\mathrm{y}^{\mathrm{2}} −\mathrm{4x}^{\mathrm{2}} =\mathrm{5}\rightarrow\mathrm{P}\left(−\mathrm{1},\mathrm{3}\right) \\ $$$$\left.\mathrm{3}\right).\:\:\mathrm{2x}^{\mathrm{3}} −\mathrm{x}^{\mathrm{2}} \mathrm{y}+\mathrm{y}^{\mathrm{3}} −\mathrm{1}=\mathrm{0}\rightarrow\mathrm{P}\left(\mathrm{2},−\mathrm{3}\right) \\ $$$$\left.\mathrm{4}\right).\:\:\mathrm{3y}^{\mathrm{4}} +\mathrm{4x}−\mathrm{x}^{\mathrm{2}} \mathrm{sin}\:\mathrm{y}−\mathrm{4}=\mathrm{0}\rightarrow\mathrm{P}\left(\mathrm{1},\mathrm{0}\right) \\ $$$$\left.\mathrm{5}\right).\:\:\mathrm{y}^{\mathrm{4}} +\mathrm{3}\:\mathrm{y}−\mathrm{4x}^{\mathrm{2}} =\mathrm{5x}+\mathrm{1}\rightarrow\mathrm{P}\left(\mathrm{1},−\mathrm{2}\right) \\ $$

Question Number 156103    Answers: 0   Comments: 0

Question Number 156102    Answers: 0   Comments: 0

Question Number 156086    Answers: 0   Comments: 4

ψ^((1)) ((1/6)) - ψ^((1)) ((5/6)) = 10ψ^((1)) ((1/3)) - ((20)/3)π^2

$$\psi^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{1}}{\mathrm{6}}\right)\:-\:\psi^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{5}}{\mathrm{6}}\right)\:=\:\mathrm{10}\psi^{\left(\mathrm{1}\right)} \left(\frac{\mathrm{1}}{\mathrm{3}}\right)\:-\:\frac{\mathrm{20}}{\mathrm{3}}\pi^{\mathrm{2}} \\ $$$$ \\ $$

Question Number 156085    Answers: 0   Comments: 0

Solve for real numbers: (sin2x + 4cos^2 x + 1)(cos5x - cosx)<0

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\left(\mathrm{sin2x}\:+\:\mathrm{4cos}^{\mathrm{2}} \mathrm{x}\:+\:\mathrm{1}\right)\left(\mathrm{cos5x}\:-\:\mathrm{cosx}\right)<\mathrm{0} \\ $$$$ \\ $$

Question Number 156082    Answers: 0   Comments: 0

0< α <(π/2) (( sin(α)))^(1/( 3)) + ((cos(α))^(1/3) )= (( tan(α)))^(1/3) (( tan (α ) + cot (α ))/2) =?

$$ \\ $$$$\:\:\:\:\:\mathrm{0}<\:\alpha\:<\frac{\pi}{\mathrm{2}}\:\:\: \\ $$$$\left.\:\:\sqrt[{\:\mathrm{3}}]{\:{sin}\left(\alpha\right)}\:+\:\sqrt[{\mathrm{3}}]{{cos}\left(\alpha\right.}\right)=\:\sqrt[{\mathrm{3}}]{\:{tan}\left(\alpha\right)} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\frac{\:{tan}\:\left(\alpha\:\right)\:+\:{cot}\:\left(\alpha\:\right)}{\mathrm{2}}\:=? \\ $$

Question Number 156080    Answers: 0   Comments: 1

∫e^(−2x) cos(e^(−x) )dx

$$\int{e}^{−\mathrm{2}{x}} {cos}\left({e}^{−{x}} \right){dx} \\ $$

Question Number 156072    Answers: 0   Comments: 5

Question Number 156065    Answers: 0   Comments: 0

find the minimum of expression M=cos((A−B)/2)sin(A/2)sin(B/2)

$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{expression}\:\mathrm{M}=\boldsymbol{\mathrm{cos}}\frac{\boldsymbol{\mathrm{A}}−\boldsymbol{\mathrm{B}}}{\mathrm{2}}\mathrm{sin}\frac{\boldsymbol{\mathrm{A}}}{\mathrm{2}}\mathrm{sin}\frac{\boldsymbol{\mathrm{B}}}{\mathrm{2}} \\ $$

Question Number 156063    Answers: 3   Comments: 2

(2/x)+(3/(x+1))+(4/(x+2))+(5/(x+3))+(6/(x+4))=5

$$\:\:\:\:\frac{\mathrm{2}}{\mathrm{x}}+\frac{\mathrm{3}}{\mathrm{x}+\mathrm{1}}+\frac{\mathrm{4}}{\mathrm{x}+\mathrm{2}}+\frac{\mathrm{5}}{\mathrm{x}+\mathrm{3}}+\frac{\mathrm{6}}{\mathrm{x}+\mathrm{4}}=\mathrm{5} \\ $$

Question Number 156077    Answers: 1   Comments: 0

Question Number 156061    Answers: 2   Comments: 0

Question Number 156059    Answers: 1   Comments: 1

Question Number 156058    Answers: 1   Comments: 0

cos(π/8)=...? with solution plz

$$\:\:{cos}\frac{\pi}{\mathrm{8}}=...?\:\:{with}\:{solution}\:{plz} \\ $$

Question Number 156052    Answers: 0   Comments: 0

Question Number 156049    Answers: 0   Comments: 0

Question Number 156047    Answers: 0   Comments: 4

Question Number 156028    Answers: 1   Comments: 0

Ω := ∫_0 ^( (π/2)) (√(sin(x))) ln(sin( x ))dx=? m.n..

$$ \\ $$$$\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \sqrt{{sin}\left({x}\right)}\:\mathrm{ln}\left({sin}\left(\:{x}\:\right)\right){dx}=? \\ $$$$\:\:{m}.{n}.. \\ $$$$ \\ $$

Question Number 156024    Answers: 1   Comments: 0

Question Number 156021    Answers: 0   Comments: 0

Question Number 156009    Answers: 0   Comments: 5

Please calculate 1). ∫sin^5 x dx 2). ∫cos^2 x dx 3). ∫tan^3 x.sec^5 x dx 4). ∫cos 5x.cos 3x dx 5). ∫ ((tan^2 x−1)/(sec^2 x)) dx

$$\mathrm{Please}\:\mathrm{calculate} \\ $$$$\left.\mathrm{1}\right).\:\int\mathrm{sin}\:^{\mathrm{5}} \mathrm{x}\:\mathrm{dx} \\ $$$$\left.\mathrm{2}\right).\:\int\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx} \\ $$$$\left.\mathrm{3}\right).\:\int\mathrm{tan}\:^{\mathrm{3}} \mathrm{x}.\mathrm{sec}\:^{\mathrm{5}} \mathrm{x}\:\mathrm{dx} \\ $$$$\left.\mathrm{4}\right).\:\int\mathrm{cos}\:\mathrm{5x}.\mathrm{cos}\:\mathrm{3x}\:\mathrm{dx} \\ $$$$\left.\mathrm{5}\right).\:\int\:\:\frac{\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}−\mathrm{1}}{\mathrm{sec}\:^{\mathrm{2}} \:\mathrm{x}}\:\:\mathrm{dx} \\ $$

Question Number 156008    Answers: 0   Comments: 8

Tekhnic Integration by part 1) Find ∫x.sec^2 x dx 2) Find ∫x.e^(2x) dx 3) Find ∫ln x dx 4) Find ∫x^2 .e^(2x) dx 5) Find ∫e^x cos x dx

$$\mathrm{Tekhnic}\:\:\mathrm{Integration}\:\mathrm{by}\:\mathrm{part} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Find}\:\int\mathrm{x}.\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{Find}\:\int\mathrm{x}.\mathrm{e}^{\mathrm{2x}} \:\mathrm{dx} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{Find}\:\int\mathrm{ln}\:\:\mathrm{x}\:\mathrm{dx} \\ $$$$\left.\mathrm{4}\right)\:\:\mathrm{Find}\:\int\mathrm{x}^{\mathrm{2}} .\mathrm{e}^{\mathrm{2x}} \:\mathrm{dx} \\ $$$$\left.\mathrm{5}\right)\:\:\mathrm{Find}\:\int\mathrm{e}^{\mathrm{x}} \:\mathrm{cos}\:\mathrm{x}\:\mathrm{dx} \\ $$$$\: \\ $$$$ \\ $$

Question Number 156005    Answers: 2   Comments: 2

∫_0 ^( (π/2)) (x/(sin(x))) dx

$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{{x}}{{sin}\left({x}\right)}\:{dx} \\ $$

Question Number 156055    Answers: 1   Comments: 0

Question Number 155996    Answers: 1   Comments: 0

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