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Question Number 62924 Answers: 1 Comments: 2

find min_((a,b)∈R^2 ) ∫_(−1) ^1 (ax+b)^2 dx

$${find}\:{min}_{\left({a},{b}\right)\in{R}^{\mathrm{2}} } \:\:\:\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \left({ax}+{b}\right)^{\mathrm{2}} {dx} \\ $$

Question Number 62919 Answers: 0 Comments: 1

kelvin and price were contesting for an election in the year 2016, kelvin lost the election and prince won the election thursday of the second week of December. After how many days will prince win the election again on thursday if the eletion is postponed to the first week of january. suppose (kelvin continious to loose the eletion again in the next four years to come). please help me solve this quetion

$$\mathrm{kelvin}\:\mathrm{and}\:\mathrm{price}\:\mathrm{were}\:\mathrm{contesting}\:\mathrm{for}\:\mathrm{an} \\ $$$$\mathrm{election}\:\mathrm{in}\:\mathrm{the}\:\mathrm{year}\:\mathrm{2016},\:\mathrm{kelvin}\:\mathrm{lost}\:\mathrm{the} \\ $$$$\mathrm{election}\:\mathrm{and}\:\:\mathrm{prince}\:\mathrm{won}\:\mathrm{the}\:\mathrm{election}\:\mathrm{thursday} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{second}\:\mathrm{week}\:\mathrm{of}\:\mathrm{December}.\:\mathrm{After} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{days}\:\mathrm{will}\:\mathrm{prince}\:\mathrm{win}\:\mathrm{the}\:\mathrm{election} \\ $$$$\mathrm{again}\:\mathrm{on}\:\mathrm{thursday}\:\mathrm{if}\:\mathrm{the}\:\mathrm{eletion}\:\mathrm{is}\:\mathrm{postponed}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{first}\:\mathrm{week}\:\mathrm{of}\:\mathrm{january}.\:\mathrm{suppose}\:\left(\mathrm{kelvin}\:\mathrm{continious}\right. \\ $$$$\mathrm{to}\:\mathrm{loose}\:\mathrm{the}\:\mathrm{eletion}\:\mathrm{again}\:\mathrm{in}\:\mathrm{the}\:\mathrm{next}\:\mathrm{four} \\ $$$$\left.\mathrm{years}\:\mathrm{to}\:\mathrm{come}\right).\: \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{quetion} \\ $$

Question Number 62914 Answers: 1 Comments: 0

Question Number 62912 Answers: 1 Comments: 0

Question Number 62962 Answers: 0 Comments: 0

P(x)=tan^(−1) (x)=Σ_(n=0) ^∞ (((−1)^n x^(2n+1) )/(2n+1)) P_(1000) (x)=? what is this sum in terms of x?

$${P}\left({x}\right)=\mathrm{tan}^{−\mathrm{1}} \left({x}\right)=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{2}{n}+\mathrm{1}}\: \\ $$$${P}_{\mathrm{1000}} \left({x}\right)=?\:{what}\:{is}\:{this}\:{sum}\:{in}\:{terms}\:{of}\:{x}? \\ $$

Question Number 62908 Answers: 0 Comments: 1

∫((arctan(x))/x)dx

$$\int\frac{{arctan}\left({x}\right)}{{x}}{dx} \\ $$

Question Number 62907 Answers: 1 Comments: 1

∫(√(((1+x)/(1−x)) ))(1+x) dx

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

Question Number 62923 Answers: 2 Comments: 0

Question Number 62906 Answers: 0 Comments: 3

∫x^x dx

$$\int\mathrm{x}^{\mathrm{x}} \mathrm{dx} \\ $$

Question Number 62895 Answers: 1 Comments: 2

Question Number 62885 Answers: 0 Comments: 0

Question Number 62889 Answers: 1 Comments: 0

Question Number 62882 Answers: 0 Comments: 3

let f(x)=ln∣((x−1)/(x+1))∣ 1)determine D_f 2) calculatef^((n)) (x) and f^((n)) (0) 3) developp f at integr serie 4) calculate ∫_(−(1/2)) ^(1/2) f(x)dx .

$${let}\:{f}\left({x}\right)={ln}\mid\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\mid \\ $$$$\left.\mathrm{1}\right){determine}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:{calculatef}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{−\frac{\mathrm{1}}{\mathrm{2}}} ^{\frac{\mathrm{1}}{\mathrm{2}}} {f}\left({x}\right){dx}\:. \\ $$

Question Number 62880 Answers: 0 Comments: 1

when f(E^c ) is equal to (f(E))^c

$${when}\:\:{f}\left({E}^{{c}} \right)\:{is}\:{equal}\:{to}\:\left({f}\left({E}\right)\right)^{{c}} \\ $$

Question Number 62879 Answers: 1 Comments: 0

calculate min Σ_(0≤i≤n and 0≤j≤n) (i+j)

$${calculate}\:{min}\:\sum_{\mathrm{0}\leqslant{i}\leqslant{n}\:\:{and}\:\mathrm{0}\leqslant{j}\leqslant{n}} \:\left({i}+{j}\right) \\ $$

Question Number 62878 Answers: 1 Comments: 0

calculate min Σ_(0≤i≤n and 0≤j≤n) i.j

$${calculate}\:{min}\:\sum_{\mathrm{0}\leqslant{i}\leqslant{n}\:{and}\:\mathrm{0}\leqslant{j}\leqslant{n}} \:\:\:\:{i}.{j} \\ $$

Question Number 62877 Answers: 0 Comments: 1

calculate lim_(n→+∞) Σ_(k=0) ^(2n+1) (n/(n^2 +k))

$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\sum_{{k}=\mathrm{0}} ^{\mathrm{2}{n}+\mathrm{1}} \:\frac{{n}}{{n}^{\mathrm{2}} \:+{k}} \\ $$

Question Number 62874 Answers: 0 Comments: 3

lim_(x→0) ((sin(6x))/(tan(5x))) how to solve this w/o L′hospital′s rule?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{sin}\left(\mathrm{6}{x}\right)}{{tan}\left(\mathrm{5}{x}\right)} \\ $$$$ \\ $$$${how}\:\:{to}\:\:{solve}\:\:{this}\:\:{w}/{o}\:\:{L}'{hospital}'{s}\:\:{rule}? \\ $$

Question Number 62861 Answers: 3 Comments: 10

Question Number 62869 Answers: 1 Comments: 0

y(dy/dx) − (y/(dy/dx)) = 2a a is a real number

$${y}\frac{{dy}}{{dx}}\:−\:\frac{{y}}{\frac{{dy}}{{dx}}}\:=\:\mathrm{2}{a} \\ $$$$ \\ $$$${a}\:{is}\:{a}\:{real}\:{number} \\ $$

Question Number 62856 Answers: 0 Comments: 3

let f(λ) =∫_0 ^(+∞) (x^4 /(x^6 +λ^6 )) dx with λ>0 1) calculate f(λ) 2) calculate also g(λ) =∫_0 ^∞ (x^4 /((x^6 +λ^6 )^2 ))dx 3) find the values of ∫_0 ^∞ (x^4 /(x^6 +1)) dx , ∫_0 ^∞ (x^4 /(x^6 +8))dx and ∫_0 ^∞ (x^4 /((x^6 +8)^2 ))dx.

$${let}\:{f}\left(\lambda\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{x}^{\mathrm{4}} }{{x}^{\mathrm{6}} \:+\lambda^{\mathrm{6}} }\:{dx}\:\:\:{with}\:\lambda>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{f}\left(\lambda\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{also}\:{g}\left(\lambda\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}^{\mathrm{4}} }{\left({x}^{\mathrm{6}} \:+\lambda^{\mathrm{6}} \right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{4}} }{{x}^{\mathrm{6}} \:+\mathrm{1}}\:{dx}\:,\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{4}} }{{x}^{\mathrm{6}} \:+\mathrm{8}}{dx}\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{4}} }{\left({x}^{\mathrm{6}} +\mathrm{8}\right)^{\mathrm{2}} }{dx}. \\ $$

Question Number 62855 Answers: 0 Comments: 1

find ∫ ((x^4 /(1+x^6 )))^2 dx 2) calculate ∫_0 ^1 (x^8 /((1+x^6 )^2 ))dx 3) calculate ∫_0 ^(+∞) (x^8 /((1+x^6 )^2 ))dx .

$${find}\:\int\:\:\left(\frac{{x}^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{6}} }\right)^{\mathrm{2}} \:{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{x}^{\mathrm{8}} }{\left(\mathrm{1}+{x}^{\mathrm{6}} \right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{x}^{\mathrm{8}} }{\left(\mathrm{1}+{x}^{\mathrm{6}} \right)^{\mathrm{2}} }{dx}\:. \\ $$

Question Number 62850 Answers: 1 Comments: 1

Question Number 62844 Answers: 1 Comments: 0

Let p(x) = ax^2 + bx + c be such that p(x) takes real values for real values of x and non−real values for non−real values of x . Prove that a = 0 and find all possible values of c.

$${Let}\:{p}\left({x}\right)\:=\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:\:{be}\:{such}\:{that}\:{p}\left({x}\right)\:{takes}\:{real}\:{values} \\ $$$${for}\:{real}\:{values}\:{of}\:{x}\:{and}\:{non}−{real}\:{values}\:{for}\:{non}−{real} \\ $$$${values}\:{of}\:{x}\:.\:{Prove}\:{that}\:{a}\:=\:\mathrm{0}\:{and}\:{find}\:{all} \\ $$$${possible}\:{values}\:{of}\:{c}. \\ $$

Question Number 62839 Answers: 1 Comments: 3

Question Number 62836 Answers: 0 Comments: 0

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