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Question Number 117205 Answers: 0 Comments: 0

∫_0 ^( 2π) ((cos^2 3x)/(1−2a∙cosx+a^2 ))dx − ? (a∈C/{−1; 1}) I need a solution through complex analysis

$$\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \frac{\boldsymbol{{cos}}^{\mathrm{2}} \mathrm{3}\boldsymbol{{x}}}{\mathrm{1}−\mathrm{2}\boldsymbol{{a}}\centerdot\boldsymbol{{cosx}}+\boldsymbol{{a}}^{\mathrm{2}} }\boldsymbol{{dx}}\:−\:?\:\left(\boldsymbol{{a}}\in\boldsymbol{{C}}/\left\{−\mathrm{1};\:\mathrm{1}\right\}\right) \\ $$$$\boldsymbol{{I}}\:\boldsymbol{{need}}\:\boldsymbol{{a}}\:\boldsymbol{{solution}}\:\boldsymbol{{through}}\:\boldsymbol{{complex}}\:\boldsymbol{{analysis}} \\ $$

Question Number 116965 Answers: 1 Comments: 0

Σ_(k=1) ^∞ (−1)^(k+1) ((sin(kθ))/(kθ))

$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} \:\frac{{sin}\left({k}\theta\right)}{{k}\theta} \\ $$

Question Number 116902 Answers: 0 Comments: 0

Question Number 116822 Answers: 3 Comments: 1

what the value of (√i) =?

$$\:\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\sqrt{{i}}\:=? \\ $$

Question Number 116685 Answers: 1 Comments: 0

Given the equality: 1+3+5+...+(2p+1)=(p+1)^(2 ) p ∈ N^∗ Show this equality is true when we replace p by p+1

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{equality}: \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{5}+...+\left(\mathrm{2p}+\mathrm{1}\right)=\left(\mathrm{p}+\mathrm{1}\right)^{\mathrm{2}\:} \:\:\:\mathrm{p}\:\in\:\mathbb{N}^{\ast} \\ $$$$ \\ $$$$\mathrm{Show}\:\mathrm{this}\:\mathrm{equality}\:\mathrm{is}\:\mathrm{true}\:\mathrm{when} \\ $$$$\mathrm{we}\:\mathrm{replace}\:\mathrm{p}\:\mathrm{by}\:\mathrm{p}+\mathrm{1} \\ $$

Question Number 116610 Answers: 1 Comments: 1

solve : ((1/( (√2))))^(2h) + (((√3)/2))^h = 1

$$ \\ $$$$\:\:\:\:\:{solve}\:: \\ $$$$\:\:\:\:\:\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right)^{\mathrm{2}{h}} \:+\:\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\right)^{{h}} \:=\:\mathrm{1} \\ $$

Question Number 116480 Answers: 1 Comments: 0

(1/8)+(1/(18))+(1/(30))+(1/(44))+(1/(60))+(1/(78))+(1/(98))+(1/(120))+........

$$\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{18}}+\frac{\mathrm{1}}{\mathrm{30}}+\frac{\mathrm{1}}{\mathrm{44}}+\frac{\mathrm{1}}{\mathrm{60}}+\frac{\mathrm{1}}{\mathrm{78}}+\frac{\mathrm{1}}{\mathrm{98}}+\frac{\mathrm{1}}{\mathrm{120}}+........ \\ $$

Question Number 116443 Answers: 0 Comments: 0

Question Number 116348 Answers: 1 Comments: 2

Find the minimum value of (((5+x)(2+x)^2 )/(x(1+x))) (x≠−1,0)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\frac{\left(\mathrm{5}+\mathrm{x}\right)\left(\mathrm{2}+\mathrm{x}\right)^{\mathrm{2}} }{\mathrm{x}\left(\mathrm{1}+\mathrm{x}\right)}\:\:\left(\mathrm{x}\neq−\mathrm{1},\mathrm{0}\right) \\ $$

Question Number 115732 Answers: 0 Comments: 1

Question Number 115696 Answers: 0 Comments: 4

e^x =logx

$$\mathrm{e}^{\mathrm{x}} =\mathrm{logx} \\ $$

Question Number 115632 Answers: 1 Comments: 6

Question Number 115487 Answers: 0 Comments: 3

Question Number 115298 Answers: 1 Comments: 2

(d^2 y/dx^2 )+log(y)=0

$$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }+\mathrm{log}\left(\mathrm{y}\right)=\mathrm{0} \\ $$

Question Number 115285 Answers: 0 Comments: 0

...♠nice topology ♠... suppose ⟨S , τ ⟩ is Baire′s space and S = ∪_(n=1) ^∞ F_n such that F_n ′s are closed sets prove that:: ∃ m ; F_m ^( °) ≠ ∅ ..m.n.july ...♣m.n.july.1970♣...

$$\:\:\:\:\:\:\:\:...\spadesuit{nice}\:\:\:{topology}\:\spadesuit... \\ $$$${suppose}\:\:\langle{S}\:,\:\tau\:\rangle\:{is}\:\:{Baire}'{s} \\ $$$${space}\:\:\:{and}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{S}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\cup}}{F}_{{n}} \:\:\:{such} \\ $$$${that}\:\:{F}_{{n}} '{s}\:\:{are}\:{closed}\:{sets}\: \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\exists\:{m}\:;\:{F}_{{m}} ^{\:°} \:\neq\:\varnothing\:\:\:..{m}.{n}.{july} \\ $$$$\:\:\:\:\:\:\:\:\:...\clubsuit{m}.{n}.{july}.\mathrm{1970}\clubsuit... \\ $$

Question Number 115237 Answers: 2 Comments: 0

Question Number 115117 Answers: 1 Comments: 0

What is the value of a and b when 3x^4 +6x^3 −ax^2 −bx−12 is completely divisible by x^2 −3 ?

$${What}\:{is}\:{the}\:{value}\:{of}\:{a}\:{and}\:{b}\:{when}\: \\ $$$$\mathrm{3}{x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{3}} −{ax}^{\mathrm{2}} −{bx}−\mathrm{12}\:{is}\:{completely} \\ $$$${divisible}\:{by}\:{x}^{\mathrm{2}} −\mathrm{3}\:? \\ $$

Question Number 114682 Answers: 1 Comments: 0

Question Number 114615 Answers: 1 Comments: 0

Question Number 114561 Answers: 1 Comments: 0

Question Number 114433 Answers: 1 Comments: 0

find sum of the series 1^2 −3^2 +5^2 −7^2 +9^2 −11^2 +...+(4n−3)^2 −(4n−1)^2

$${find}\:{sum}\:{of}\:{the}\:{series}\: \\ $$$$\mathrm{1}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} +\mathrm{9}^{\mathrm{2}} −\mathrm{11}^{\mathrm{2}} +...+\left(\mathrm{4}{n}−\mathrm{3}\right)^{\mathrm{2}} −\left(\mathrm{4}{n}−\mathrm{1}\right)^{\mathrm{2}} \\ $$

Question Number 114343 Answers: 0 Comments: 4

How many ways can we place 5 identical books and another 6 identical books on a shelf?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{we}\:\mathrm{place}\:\mathrm{5}\:\mathrm{identical} \\ $$$$\mathrm{books}\:\mathrm{and}\:\mathrm{another}\:\mathrm{6}\:\mathrm{identical}\:\mathrm{books} \\ $$$$\mathrm{on}\:\mathrm{a}\:\mathrm{shelf}? \\ $$

Question Number 114032 Answers: 0 Comments: 0

Question Number 113897 Answers: 1 Comments: 0

Question Number 113756 Answers: 2 Comments: 1

∫_0 ^1 ((log(x+1))/x)dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{log}\left({x}+\mathrm{1}\right)}{{x}}{dx} \\ $$

Question Number 113637 Answers: 0 Comments: 0

Montrer que pour 0<z<1 on a Γ(z)Γ(1−z)=(π/(sin(πz)))

$${Montrer}\:{que}\:{pour}\:\mathrm{0}<{z}<\mathrm{1}\:{on}\:{a} \\ $$$$\Gamma\left({z}\right)\Gamma\left(\mathrm{1}−{z}\right)=\frac{\pi}{{sin}\left(\pi{z}\right)} \\ $$

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