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Question Number 49343 Answers: 0 Comments: 1

find ∫_0 ^1 ((ln(x))/(1+x))dx .

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left({x}\right)}{\mathrm{1}+{x}}{dx}\:. \\ $$

Question Number 49342 Answers: 0 Comments: 0

find ∫_0 ^1 (e^x /(1+x))dx .

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{e}^{{x}} }{\mathrm{1}+{x}}{dx}\:. \\ $$

Question Number 49340 Answers: 0 Comments: 0

Question Number 49333 Answers: 0 Comments: 0

Question Number 49331 Answers: 1 Comments: 2

Find : arg( (((2(√3)+2i)^8 )/((1−i)^6 )) + (((1+i)^6 )/((2(√3)−2i)^8 ))) ?

$${Find}\:: \\ $$$${arg}\left(\:\frac{\left(\mathrm{2}\sqrt{\mathrm{3}}+\mathrm{2}{i}\right)^{\mathrm{8}} }{\left(\mathrm{1}−{i}\right)^{\mathrm{6}} }\:\:+\:\frac{\left(\mathrm{1}+{i}\right)^{\mathrm{6}} }{\left(\mathrm{2}\sqrt{\mathrm{3}}−\mathrm{2}{i}\right)^{\mathrm{8}} }\right)\:? \\ $$

Question Number 49326 Answers: 0 Comments: 0

please help me! { ((u_1 =a, u_2 =b)),((u_(n+2) =3(u_(n+1) )^(1/5) +13(u_n )^(1/5) ,n∈N^∗ )) :} show that (u_n ) have limit and find its limit.

$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}! \\ $$$$\begin{cases}{\mathrm{u}_{\mathrm{1}} ={a},\:\mathrm{u}_{\mathrm{2}} =\mathrm{b}}\\{\mathrm{u}_{\mathrm{n}+\mathrm{2}} =\mathrm{3}\sqrt[{\mathrm{5}}]{\mathrm{u}_{\mathrm{n}+\mathrm{1}} }+\mathrm{13}\sqrt[{\mathrm{5}}]{\mathrm{u}_{\mathrm{n}} }\:,\mathrm{n}\in\mathbb{N}^{\ast} }\end{cases} \\ $$$$\mathrm{show}\:\mathrm{that}\:\left(\mathrm{u}_{\mathrm{n}} \right)\:\mathrm{have}\:\mathrm{limit}\:\mathrm{and}\:\mathrm{find}\: \\ $$$$\mathrm{its}\:\mathrm{limit}. \\ $$

Question Number 49337 Answers: 0 Comments: 0

Question Number 49299 Answers: 3 Comments: 3

Question Number 49296 Answers: 2 Comments: 0

Question Number 49298 Answers: 4 Comments: 0

Question Number 49294 Answers: 1 Comments: 0

Question Number 49283 Answers: 1 Comments: 0

Question Number 49280 Answers: 1 Comments: 3

Question Number 49272 Answers: 2 Comments: 0

ZεC satisfies the condition ∣Z∣≥3. Then find the least value of ∣Z+(1/Z)∣ ?

$${Z}\epsilon\mathbb{C}\:{satisfies}\:{the}\:{condition}\:\mid{Z}\mid\geqslant\mathrm{3}. \\ $$$${Then}\:{find}\:{the}\:{least}\:{value}\:{of}\:\mid{Z}+\frac{\mathrm{1}}{{Z}}\mid\:? \\ $$

Question Number 49279 Answers: 2 Comments: 1

Question Number 49256 Answers: 2 Comments: 0

Question Number 49253 Answers: 2 Comments: 0

Question Number 49252 Answers: 1 Comments: 0

Question Number 49251 Answers: 5 Comments: 1

Question Number 49250 Answers: 1 Comments: 0

Apply derivative criteria F(x)=x^3 +5x^2 −2x+3

$${Apply}\:{derivative}\:{criteria} \\ $$$${F}\left({x}\right)={x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{3} \\ $$

Question Number 49248 Answers: 1 Comments: 0

1) solve z^4 =1+i(√3) 2) factorize p(x)=x^4 −1−i(√3)inside C[x] 3)factorze inside R[x] the polynom p(x).

$$\left.\mathrm{1}\right)\:{solve}\:{z}^{\mathrm{4}} =\mathrm{1}+{i}\sqrt{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{p}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{1}−{i}\sqrt{\mathrm{3}}{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right){factorze}\:{inside}\:{R}\left[{x}\right]\:{the}\:{polynom}\:{p}\left({x}\right). \\ $$

Question Number 49244 Answers: 1 Comments: 0

let w from C and w^n =1 find the value of S =Σ_(k=0) ^(n−1) C_n ^k w^k .

$${let}\:{w}\:{from}\:{C}\:{and}\:{w}^{{n}} \:=\mathrm{1}\:{find}\:{the}\:{value}\:{of}\: \\ $$$${S}\:=\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{C}_{{n}} ^{{k}} \:{w}^{{k}} \:. \\ $$

Question Number 49246 Answers: 0 Comments: 0

simplify Π_(k=0) ^(n−1) (e^(i((4kπ)/n)) −2cosθ e^((i2π)/n) +1)

$${simplify}\:\:\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \left({e}^{{i}\frac{\mathrm{4}{k}\pi}{{n}}} \:−\mathrm{2}{cos}\theta\:{e}^{\frac{{i}\mathrm{2}\pi}{{n}}} \:+\mathrm{1}\right) \\ $$

Question Number 49245 Answers: 0 Comments: 0

solve inside C: 1+(z−1)^3 +(z−1)^6 =0

$${solve}\:{inside}\:{C}:\:\mathrm{1}+\left({z}−\mathrm{1}\right)^{\mathrm{3}} \:+\left({z}−\mathrm{1}\right)^{\mathrm{6}} =\mathrm{0} \\ $$

Question Number 49242 Answers: 0 Comments: 0

let z from C and θ from R and z^2 +2zcosθ +1 =0 find the value of z^(2n) +2zcos(nθ)+1 .

$${let}\:{z}\:{from}\:{C}\:{and}\:\theta\:{from}\:{R}\:{and}\:{z}^{\mathrm{2}} \:+\mathrm{2}{zcos}\theta\:+\mathrm{1}\:=\mathrm{0}\:{find}\:{the}\:{value}\:{of} \\ $$$${z}^{\mathrm{2}{n}} \:+\mathrm{2}{zcos}\left({n}\theta\right)+\mathrm{1}\:. \\ $$$$ \\ $$

Question Number 49241 Answers: 0 Comments: 0

let z =r e^(iθ) find the value of P_n =(z+z^− )(z^2 +z^−^2 ).....(z^n +z^−^n ) .

$${let}\:{z}\:={r}\:{e}^{{i}\theta} \:\:\:{find}\:{the}\:{value}\:{of}\: \\ $$$${P}_{{n}} =\left({z}+\overset{−} {{z}}\right)\left({z}^{\mathrm{2}} \:+\overset{−^{\mathrm{2}} } {{z}}\right).....\left({z}^{{n}} \:+\overset{−^{{n}} } {{z}}\right)\:. \\ $$

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