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Question Number 158469 Answers: 2 Comments: 0

find the maclaurin series expension for the function f(x) = sin^2 x ; x_o = 0

$${find}\:{the}\:{maclaurin}\:{series}\:{expension} \\ $$$${for}\:{the}\:{function}\:{f}\left({x}\right)\:=\:{sin}^{\mathrm{2}} {x}\:;\:\:\:\:\:\:{x}_{{o}} =\:\mathrm{0} \\ $$

Question Number 158465 Answers: 1 Comments: 0

Question Number 158455 Answers: 1 Comments: 0

Question Number 158450 Answers: 0 Comments: 0

Demontrer que minN=0

$$\mathrm{Demontrer}\:\mathrm{que}\:\mathrm{min}\mathbb{N}=\mathrm{0} \\ $$

Question Number 158444 Answers: 1 Comments: 5

if x and y are positive integers with ((2010)/(2011)) < (x/y) < ((2011)/(2012)) then compute the minimum value for x+y and the values of x and y which achieves this minimum

$$\mathrm{if}\:\:\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}}\:\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{with} \\ $$$$\frac{\mathrm{2010}}{\mathrm{2011}}\:<\:\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{y}}}\:<\:\frac{\mathrm{2011}}{\mathrm{2012}}\:\:\mathrm{then}\:\mathrm{compute}\:\mathrm{the} \\ $$$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{for}\:\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\:\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{values}\:\mathrm{of}\:\:\boldsymbol{\mathrm{x}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{y}}\:\:\mathrm{which}\:\mathrm{achieves} \\ $$$$\mathrm{this}\:\mathrm{minimum} \\ $$

Question Number 158443 Answers: 1 Comments: 0

How many divisors has the positive integer n which verify n^n = 2027^(2027^(2028) ) ?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{divisors}\:\mathrm{has}\:\mathrm{the}\:\mathrm{positive} \\ $$$$\mathrm{integer}\:\:\boldsymbol{\mathrm{n}}\:\:\mathrm{which}\:\mathrm{verify} \\ $$$$\mathrm{n}^{\boldsymbol{\mathrm{n}}} \:=\:\mathrm{2027}^{\mathrm{2027}^{\mathrm{2028}} } \:? \\ $$

Question Number 158438 Answers: 1 Comments: 2

Question Number 158437 Answers: 0 Comments: 0

Question Number 158410 Answers: 2 Comments: 0

Question Number 158405 Answers: 2 Comments: 0

prove: ∫_0 ^∞ (1/(x^5 +x^4 +x^3 +x^2 +x+1))dx=(π/(3(√3)))

$${prove}: \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{{x}^{\mathrm{5}} +{x}^{\mathrm{4}} +{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx}=\frac{\pi}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$

Question Number 158403 Answers: 0 Comments: 0

Question Number 158402 Answers: 0 Comments: 0

∫_((1;π)) ^((2;π)) (1−(y^2 /x^2 )cos((y/x)))dx+(sin((y/x))+(y/x)cos((y/x)))dy=?

$$\int_{\left(\mathrm{1};\pi\right)} ^{\left(\mathrm{2};\pi\right)} \left(\mathrm{1}−\frac{{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} }{cos}\left(\frac{{y}}{{x}}\right)\right){dx}+\left({sin}\left(\frac{{y}}{{x}}\right)+\frac{{y}}{{x}}{cos}\left(\frac{{y}}{{x}}\right)\right){dy}=? \\ $$

Question Number 158417 Answers: 1 Comments: 0

z^3 −(7+6i)z^2 +3(1+9i)z+2(7−9i)=0 Resolve the equation (E) sachet that the stop image one any solution behoves thru the righ t equation y=x

$${z}^{\mathrm{3}} −\left(\mathrm{7}+\mathrm{6}{i}\right){z}^{\mathrm{2}} +\mathrm{3}\left(\mathrm{1}+\mathrm{9}{i}\right){z}+\mathrm{2}\left(\mathrm{7}−\mathrm{9}{i}\right)=\mathrm{0} \\ $$$${Resolve}\:{the}\:{equation}\:\left({E}\right)\:{sachet}\:{that}\: \\ $$$${the}\:{stop}\:{image}\:\:{one}\:{any}\:{solution}\:{behoves} \\ $$$${thru}\:{the}\:{righ}\:{t}\:{equation}\:{y}={x} \\ $$

Question Number 158420 Answers: 1 Comments: 0

∫_0 ^∞ ((lnx)/(1−x^2 ))dx

$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{lnx}}{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 158419 Answers: 0 Comments: 0

Question Number 158396 Answers: 1 Comments: 0

Any proof or Idea about; (4/2)÷((16)/3) = (4/2)×(3/(16))

$${Any}\:{proof}\:{or}\:{Idea}\:{about}; \\ $$$$\frac{\mathrm{4}}{\mathrm{2}}\boldsymbol{\div}\frac{\mathrm{16}}{\mathrm{3}}\:=\:\frac{\mathrm{4}}{\mathrm{2}}×\frac{\mathrm{3}}{\mathrm{16}} \\ $$

Question Number 158391 Answers: 2 Comments: 1

if α,β,γ are the angles of a triangle, find ((sin 2𝛂+sin 2𝛃+sin 2𝛄)/(sin 𝛂 sin 𝛃 sin 𝛄))=?

$${if}\:\alpha,\beta,\gamma\:{are}\:{the}\:{angles}\:{of}\:{a}\:{triangle}, \\ $$$${find}\:\frac{\boldsymbol{\mathrm{sin}}\:\mathrm{2}\boldsymbol{\alpha}+\boldsymbol{\mathrm{sin}}\:\mathrm{2}\boldsymbol{\beta}+\boldsymbol{\mathrm{sin}}\:\mathrm{2}\boldsymbol{\gamma}}{\boldsymbol{\mathrm{sin}}\:\boldsymbol{\alpha}\:\boldsymbol{\mathrm{sin}}\:\boldsymbol{\beta}\:\boldsymbol{\mathrm{sin}}\:\boldsymbol{\gamma}}=? \\ $$

Question Number 158383 Answers: 1 Comments: 0

Solve for real numbers: (1/(1 + tan^4 (x))) + (1/(10)) = (2/(1 + 3 tan^2 (x)))

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{tan}^{\mathrm{4}} \left(\boldsymbol{\mathrm{x}}\right)}\:+\:\frac{\mathrm{1}}{\mathrm{10}}\:=\:\frac{\mathrm{2}}{\mathrm{1}\:+\:\mathrm{3}\:\mathrm{tan}^{\mathrm{2}} \left(\boldsymbol{\mathrm{x}}\right)} \\ $$$$ \\ $$

Question Number 158379 Answers: 0 Comments: 1

F(x+1)−F(x−1)=6 F(0)=4 F(3)=?

$${F}\left({x}+\mathrm{1}\right)−{F}\left({x}−\mathrm{1}\right)=\mathrm{6} \\ $$$${F}\left(\mathrm{0}\right)=\mathrm{4} \\ $$$${F}\left(\mathrm{3}\right)=? \\ $$

Question Number 158378 Answers: 1 Comments: 0

How to graph order pair (3+5i , 4−2i)?

$${How}\:{to}\:{graph}\:{order}\:{pair}\:\left(\mathrm{3}+\mathrm{5}{i}\:,\:\mathrm{4}−\mathrm{2}{i}\right)? \\ $$

Question Number 158422 Answers: 2 Comments: 1

Question Number 158421 Answers: 2 Comments: 0

Question Number 158365 Answers: 0 Comments: 0

Question Number 158364 Answers: 0 Comments: 0

if a;b;c>0 prove that: a^(2a-(b+c)) ∙ b^(2b-(c+a)) ∙ c^(2c-(a+b)) ≥ 1

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\mathrm{a}^{\mathrm{2}\boldsymbol{\mathrm{a}}-\left(\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}\right)} \:\centerdot\:\mathrm{b}^{\mathrm{2}\boldsymbol{\mathrm{b}}-\left(\boldsymbol{\mathrm{c}}+\boldsymbol{\mathrm{a}}\right)} \:\centerdot\:\mathrm{c}^{\mathrm{2}\boldsymbol{\mathrm{c}}-\left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}\right)} \:\geqslant\:\mathrm{1} \\ $$$$ \\ $$

Question Number 158363 Answers: 1 Comments: 0

x;y;z>0 Solve for real numbers: { ((x^3 + y^3 + z^3 + 3∙((x)^(1/3) + (y)^(1/3) + (z)^(1/3) ) = 12)),((x∙y∙z = 1)) :}

$$\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0} \\ $$$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \:+\:\mathrm{3}\centerdot\left(\sqrt[{\mathrm{3}}]{\mathrm{x}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{y}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{z}}\right)\:=\:\mathrm{12}}\\{\mathrm{x}\centerdot\mathrm{y}\centerdot\mathrm{z}\:=\:\mathrm{1}}\end{cases} \\ $$$$ \\ $$

Question Number 158358 Answers: 0 Comments: 0

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