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Question Number 156201    Answers: 0   Comments: 1

A=[((x^n ((x^n^2 ((x^n^3 ∙∙∙∙(x^n^n )^(1/n) ))^(1/n) ))^(1/n) ))^(1/n) ]^(1/n)

$$\:\:{A}=\left[\sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}} \sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}^{\mathrm{2}} } \sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}^{\mathrm{3}} } \centerdot\centerdot\centerdot\centerdot\sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}^{\mathrm{n}} } }}}}\right]^{\frac{\mathrm{1}}{\mathrm{n}}} \\ $$

Question Number 156123    Answers: 0   Comments: 0

Question Number 156119    Answers: 1   Comments: 2

solve : ((1+2x)/(1+(√(1+2x))))+((1−2x)/(1−(√(1−2x))))=1

$$\mathrm{solve}\:: \\ $$$$\:\frac{\mathrm{1}+\mathrm{2x}}{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{2x}}}+\frac{\mathrm{1}−\mathrm{2x}}{\mathrm{1}−\sqrt{\mathrm{1}−\mathrm{2x}}}=\mathrm{1} \\ $$$$ \\ $$

Question Number 156109    Answers: 2   Comments: 0

log _5 ((√(x−9)))−log _5 (3x^2 −12)−log _5 ((√(2x−1))) ≤ 0

$$\:\:\mathrm{log}\:_{\mathrm{5}} \left(\sqrt{\mathrm{x}−\mathrm{9}}\right)−\mathrm{log}\:_{\mathrm{5}} \left(\mathrm{3x}^{\mathrm{2}} −\mathrm{12}\right)−\mathrm{log}\:_{\mathrm{5}} \left(\sqrt{\mathrm{2x}−\mathrm{1}}\right)\:\leqslant\:\mathrm{0} \\ $$

Question Number 156108    Answers: 0   Comments: 0

lim_(x→(π/8)) ((1+cot 6x)/(1−sin 4x)) =?

$$\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{8}}} {\mathrm{lim}}\:\frac{\mathrm{1}+\mathrm{cot}\:\mathrm{6x}}{\mathrm{1}−\mathrm{sin}\:\mathrm{4x}}\:=? \\ $$

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

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