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Question Number 40042 Answers: 0 Comments: 0

1) find the roots of p(x)=(1+ix +x^2 )^n −(1−ix+x^2 )^n with n integr natural 2) factorize p(x) inside C(x) 3) give p(x) at form Σ a_p x^p

$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:\: \\ $$$${p}\left({x}\right)=\left(\mathrm{1}+{ix}\:+{x}^{\mathrm{2}} \right)^{{n}} −\left(\mathrm{1}−{ix}+{x}^{\mathrm{2}} \right)^{{n}} \:{with}\:{n}\:{integr} \\ $$$${natural} \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{p}\left({x}\right)\:{inside}\:\:{C}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{give}\:{p}\left({x}\right)\:{at}\:{form}\:\:\Sigma\:{a}_{{p}} {x}^{{p}} \\ $$

Question Number 40040 Answers: 0 Comments: 1

let A_n = ∫_0 ^n e^(−n( x+2−[x])) dx with n integr natural 1) calculate A_n 2) find lim_(n→+∞) A_n 3) study the convergence of Σ_n A_n

$${let}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:{e}^{−{n}\left(\:{x}+\mathrm{2}−\left[{x}\right]\right)} {dx}\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{study}\:{the}\:{convergence}\:{of}\:\:\:\sum_{{n}} {A}_{{n}} \\ $$

Question Number 40037 Answers: 1 Comments: 0

Question Number 40031 Answers: 1 Comments: 1

Question Number 40023 Answers: 2 Comments: 0

Question Number 40022 Answers: 0 Comments: 2

To the developer Tinku Tara: Dear sir, can you please make it possible again that a posted image can be updated (changed) through the “edit post” function. This was possible in the past. But it is now not possible for unknown reasons. Thank you!

$${To}\:{the}\:{developer}\:{Tinku}\:{Tara}: \\ $$$${Dear}\:{sir}, \\ $$$${can}\:{you}\:{please}\:{make}\:{it}\:{possible}\:{again} \\ $$$${that}\:{a}\:{posted}\:{image}\:{can}\:{be}\:{updated} \\ $$$$\left({changed}\right)\:{through}\:{the}\:``{edit}\:{post}'' \\ $$$${function}. \\ $$$${This}\:{was}\:{possible}\:{in}\:{the}\:{past}.\:{But}\:{it}\:{is} \\ $$$${now}\:{not}\:{possible}\:{for}\:{unknown}\:{reasons}. \\ $$$${Thank}\:{you}! \\ $$

Question Number 40012 Answers: 1 Comments: 0

Question Number 40008 Answers: 1 Comments: 1

1) find ∫ (dx/((x+1)(√x) +x(√(x+1)))) .

$$\left.\mathrm{1}\right)\:{find}\:\:\int\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}}\:\:+{x}\sqrt{{x}+\mathrm{1}}}\:. \\ $$

Question Number 40007 Answers: 0 Comments: 1

find thevalue of ∫_0 ^∞ (dx/(1 +x^6 )) by using the value of ∫_(−∞) ^(+∞) (dx/(x−z)) with z ∈ C and Im(z)≠0

$${find}\:{thevalue}\:{of}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\mathrm{1}\:+{x}^{\mathrm{6}} }\:\:{by}\:{using}\:{the} \\ $$$${value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{{x}−{z}}\:{with}\:{z}\:\in\:{C}\:{and}\:{Im}\left({z}\right)\neq\mathrm{0} \\ $$$$ \\ $$

Question Number 39995 Answers: 2 Comments: 0

Question Number 39993 Answers: 2 Comments: 0

Question Number 39985 Answers: 1 Comments: 0

Question Number 39983 Answers: 1 Comments: 0

To developer,Is there any way of getting back your previous account if you lost your password?

$${To}\:{developer},{Is}\:{there}\:{any}\:{way}\:{of} \\ $$$${getting}\:{back}\:{your}\:{previous}\:{account} \\ $$$${if}\:{you}\:{lost}\:{your}\:{password}? \\ $$

Question Number 39975 Answers: 0 Comments: 4

lim_(x→∞) (((∫_( 0) ^x e^x dx)^2 )/(∫_( 0) ^x e^(2x^2 ) dx)) =

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\underset{\:\mathrm{0}} {\overset{{x}} {\int}}\:\:{e}^{{x}} \:{dx}\right)^{\mathrm{2}} }{\underset{\:\mathrm{0}} {\overset{{x}} {\int}}\:\:{e}^{\mathrm{2}{x}^{\mathrm{2}} } \:{dx}}\:\:= \\ $$

Question Number 39971 Answers: 3 Comments: 0

a>0,b>0, What is the minimum value of ((b^2 +2)/(a+b))+(a^2 /(ab+1)) ?

$${a}>\mathrm{0},{b}>\mathrm{0}, \\ $$$${What}\:{is}\:{the}\:{minimum}\:{value}\:{of} \\ $$$$\frac{{b}^{\mathrm{2}} +\mathrm{2}}{{a}+{b}}+\frac{{a}^{\mathrm{2}} }{{ab}+\mathrm{1}}\:\:\:? \\ $$

Question Number 39970 Answers: 1 Comments: 0

Question Number 39955 Answers: 1 Comments: 2

Question Number 39967 Answers: 0 Comments: 4

1) decompose inside C(x) the fraction F(x)= (3/(4+x^4 )) 2) find ∫_(−∞) ^(+∞) (dx/(x−z)) with z from C 3) find the value of ∫_(−∞) ^(+∞) ((3dx)/(4+x^4 )) .

$$\left.\mathrm{1}\right)\:{decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction} \\ $$$${F}\left({x}\right)=\:\frac{\mathrm{3}}{\mathrm{4}+{x}^{\mathrm{4}} } \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{{x}−{z}}\:\:{with}\:{z}\:{from}\:{C} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{\mathrm{3}{dx}}{\mathrm{4}+{x}^{\mathrm{4}} }\:. \\ $$

Question Number 39929 Answers: 1 Comments: 0

Question Number 39928 Answers: 0 Comments: 1

what numbers is that of which the third Part exceeds the fifth part by 4

$${what}\:{numbers}\:{is}\:{that}\:{of}\:{which}\:{the}\:{third}\:{Part}\:{exceeds}\:{the}\:{fifth}\:{part}\:{by}\:\mathrm{4} \\ $$

Question Number 39921 Answers: 4 Comments: 0

Question Number 39930 Answers: 1 Comments: 0

Question Number 39899 Answers: 0 Comments: 0

Given the lines l_1 ; 3y = 2x ,l_2 ; y = −((3x)/2) + p and l_3 ; y ^ = x + 1 a) find the value of p if the point of intersection between l_1 and l_2 is (3,5) b) find the cosine of the angle between l_2 and l_3 c) which line holds the point (1,2). d)find the line l_4 with gradient ∫_4 ^π [l_1 + l_2 dx] perpendicur to l_2 ,parrallel to l_1 .

$${Given}\:{the}\:{lines}\: \\ $$$${l}_{\mathrm{1}} ;\:\mathrm{3}{y}\:=\:\mathrm{2}{x}\:,{l}_{\mathrm{2}} ;\:{y}\:=\:−\frac{\mathrm{3}{x}}{\mathrm{2}}\:+\:{p} \\ $$$${and}\:{l}_{\mathrm{3}} ;\:{y}\overset{} {\:}=\:{x}\:+\:\mathrm{1} \\ $$$$\left.{a}\right)\:{find}\:{the}\:{value}\:{of}\:{p}\:{if}\: \\ $$$${the}\:{point}\:{of}\:{intersection}\:{between} \\ $$$${l}_{\mathrm{1}} \:{and}\:{l}_{\mathrm{2}} \:{is}\:\left(\mathrm{3},\mathrm{5}\right) \\ $$$$\left.{b}\right)\:{find}\:{the}\:{cosine}\:{of}\:{the}\:{angle} \\ $$$${between}\:{l}_{\mathrm{2}} \:{and}\:{l}_{\mathrm{3}} \\ $$$$\left.{c}\right)\:{which}\:{line}\:{holds}\:{the}\:{point} \\ $$$$\left(\mathrm{1},\mathrm{2}\right). \\ $$$$\left.{d}\right){find}\:{the}\:{line}\:{l}_{\mathrm{4}} \:{with}\:{gradient} \\ $$$$\int_{\mathrm{4}} ^{\pi} \left[{l}_{\mathrm{1}} \:+\:{l}_{\mathrm{2}} \:{dx}\right]\:{perpendicur}\:{to} \\ $$$${l}_{\mathrm{2}} ,{parrallel}\:{to}\:{l}_{\mathrm{1}} . \\ $$

Question Number 39914 Answers: 0 Comments: 1

Question Number 39892 Answers: 0 Comments: 5

let g(x)= e^(−2x) arctan(x+3) developp g at integr serie .

$${let}\:{g}\left({x}\right)=\:{e}^{−\mathrm{2}{x}} \:{arctan}\left({x}+\mathrm{3}\right) \\ $$$${developp}\:{g}\:{at}\:{integr}\:{serie}\:\:. \\ $$

Question Number 39891 Answers: 0 Comments: 5

let f(x)=arctan(2x+1) 1) calculate f^((n)) (x) 2) calculate f^((n)) (0) 3) developp f at integr serie 4) calculate ∫_0 ^1 f(x)dx 5) calculate ∫_0 ^1 ((arctan(2x+1))/(4x^2 +4x +2))dx

$${let}\:{f}\left({x}\right)={arctan}\left(\mathrm{2}{x}+\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:{f}\left({x}\right){dx} \\ $$$$\left.\mathrm{5}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{arctan}\left(\mathrm{2}{x}+\mathrm{1}\right)}{\mathrm{4}{x}^{\mathrm{2}} \:+\mathrm{4}{x}\:+\mathrm{2}}{dx} \\ $$

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