Question and Answers Forum

AllQuestion and Answers: Page 1440

Question Number 67038 Answers: 1 Comments: 1

calculate ∫_(−1) ^1 (x^(2n) /(1+2^(sinx) ))dx with n integr.

$${calculate}\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\frac{{x}^{\mathrm{2}{n}} }{\mathrm{1}+\mathrm{2}^{{sinx}} }{dx}\:\:\:{with}\:{n}\:{integr}. \\ $$

Question Number 67035 Answers: 1 Comments: 2

Question Number 67034 Answers: 0 Comments: 2

calculate Σ_(n=1) ^∞ ((cos(2nx))/n)

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{cos}\left(\mathrm{2}{nx}\right)}{{n}} \\ $$

Question Number 67033 Answers: 0 Comments: 5

Question Number 67032 Answers: 0 Comments: 0

Question Number 67031 Answers: 0 Comments: 4

lim_(x→−1) ((((x^5 )^(1/7) +1)/(1+(x^7 )^(1/(9 )) )))^(1/3) =?

$$\: \\ $$$$\:\underset{\boldsymbol{\mathrm{x}}\rightarrow−\mathrm{1}} {\boldsymbol{\mathrm{lim}}}\sqrt[{\mathrm{3}}]{\frac{\sqrt[{\mathrm{7}}]{\boldsymbol{\mathrm{x}}^{\mathrm{5}} }+\mathrm{1}}{\mathrm{1}+\sqrt[{\mathrm{9}\:}]{\boldsymbol{\mathrm{x}}^{\mathrm{7}} }}}=? \\ $$$$\: \\ $$

Question Number 67026 Answers: 0 Comments: 5

Question Number 67025 Answers: 0 Comments: 3

Question Number 67023 Answers: 1 Comments: 1

find the sequence U_n wich verify U_n +U_(n+1) =sin(n) ∀n from n

$${find}\:{the}\:{sequence}\:{U}_{{n}} \:{wich}\:{verify}\:\:{U}_{{n}} +{U}_{{n}+\mathrm{1}} ={sin}\left({n}\right)\:\:\forall{n}\:{from}\:{n} \\ $$

Question Number 67022 Answers: 0 Comments: 0

find ∫ (1+(√x))(√(x^2 +3))dx

$${find}\:\int\:\left(\mathrm{1}+\sqrt{{x}}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{3}}{dx} \\ $$

Question Number 67021 Answers: 0 Comments: 1

find f(x) =∫_0 ^1 ln(x +e^(−t) )dt with x>0

$${find}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\:+{e}^{−{t}} \right){dt}\:\:\:{with}\:{x}>\mathrm{0} \\ $$

Question Number 67020 Answers: 0 Comments: 1

find f(x) = ∫_0 ^1 arctan(1+xt)dt with x real

$${find}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left(\mathrm{1}+{xt}\right){dt}\:\:{with}\:{x}\:{real} \\ $$

Question Number 67019 Answers: 0 Comments: 0

calculate ∫_0 ^∞ e^(−x^2 ) arctan(x^2 )dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{x}^{\mathrm{2}} } {arctan}\left({x}^{\mathrm{2}} \right){dx}\: \\ $$

Question Number 67018 Answers: 0 Comments: 1

find ∫_0 ^∞ e^(−x) ln(1+x)dx

$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{x}} {ln}\left(\mathrm{1}+{x}\right){dx} \\ $$

Question Number 67017 Answers: 0 Comments: 1

find ∫ arctan(1+(√(x+1)))dx

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

Question Number 67016 Answers: 0 Comments: 0

find ∫ arctan(1+(√x)+(√(x+1)))dx

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

Question Number 67015 Answers: 0 Comments: 0

let f(x) =arctan(1+e^(−(√(1+x^2 ))) ) calculate f^′ (x) and f^(′′) (x). 1)find lim_(x→+∞) f(x) and lim_(x→−∞) f(x) 3)study the variation of f(x) 4)give the equation of tangent to C_f at A(1,f(1))

$${let}\:{f}\left({x}\right)\:={arctan}\left(\mathrm{1}+{e}^{−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \right) \\ $$$${calculate}\:{f}^{'} \left({x}\right)\:\:{and}\:{f}^{''} \left({x}\right). \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow−\infty} \:\:\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right){study}\:{the}\:{variation}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{4}\right){give}\:{the}\:{equation}\:{of}\:{tangent}\:{to}\:{C}_{{f}} \:{at}\:\:{A}\left(\mathrm{1},{f}\left(\mathrm{1}\right)\right) \\ $$

Question Number 67014 Answers: 0 Comments: 1

solve y^(′′) +x^2 y^′ =e^(−x) sin(3x)

$${solve}\:{y}^{''} +{x}^{\mathrm{2}} {y}^{'} ={e}^{−{x}} {sin}\left(\mathrm{3}{x}\right) \\ $$

Question Number 67013 Answers: 0 Comments: 1

find the value of Σ_(n=1) ^∞ (((−1)^n )/((n+1)n^3 ))

$${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left({n}+\mathrm{1}\right){n}^{\mathrm{3}} } \\ $$

Question Number 67012 Answers: 0 Comments: 1

find ∫_1 ^(+∞) ((arctan([x]))/x^3 )dx

$${find}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{arctan}\left(\left[{x}\right]\right)}{{x}^{\mathrm{3}} }{dx} \\ $$

Question Number 67011 Answers: 0 Comments: 1

calculate U_n =∫_1 ^(+∞) ((arctan(n[x]))/x^2 )dx

$${calculate}\:{U}_{{n}} =\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{arctan}\left({n}\left[{x}\right]\right)}{{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 67010 Answers: 0 Comments: 1

calculate Σ_(n=4) ^(+∞) (n/((n^2 −9)^2 ))

$${calculate}\:\:\sum_{{n}=\mathrm{4}} ^{+\infty} \:\:\:\:\frac{{n}}{\left({n}^{\mathrm{2}} −\mathrm{9}\right)^{\mathrm{2}} } \\ $$

Question Number 67008 Answers: 0 Comments: 2

let f(x) =∫_0 ^∞ (dt/((x^2 +t^2 )^2 )) with x>0 1) find a explicit form of (x) 2)find also g(x) =∫_0 ^∞ (dt/((x^2 +t^2 )^3 )) 3)find the values of integrals ∫_0 ^∞ (dt/((t^2 +3)^2 )) and ∫_0 ^∞ (dt/((t^2 +3)^3 )) 4) calculate U_θ =∫_0 ^∞ (dt/((t^2 +cos^2 θ)^2 )) with 0<θ<(π/2) 5) find f^((n)) (x) and f^((n)) (0) 6) developp f at integr serie

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dt}}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)^{\mathrm{3}} } \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{values}\:{of}\:{integrals}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left({t}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }\:{and}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dt}}{\left({t}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{3}} } \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:{U}_{\theta} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left({t}^{\mathrm{2}} \:+{cos}^{\mathrm{2}} \theta\right)^{\mathrm{2}} }\:\:\:{with}\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$$$\left.\mathrm{5}\right)\:{find}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{6}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$

Question Number 67006 Answers: 0 Comments: 1

calculae A_n =∫_0 ^∞ (dx/((x^2 +1)^n )) with n integr natural and n>0

$${calculae}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{n}} }\:\:\:{with}\:{n}\:{integr}\:{natural}\:{and}\:{n}>\mathrm{0} \\ $$

Question Number 67005 Answers: 0 Comments: 1

find ∫ ((x−2(√(x^2 −1)))/(x+2(√(x^2 −1))))dx

$${find}\:\int\:\:\:\frac{{x}−\mathrm{2}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{{x}+\mathrm{2}\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{dx} \\ $$

Question Number 67004 Answers: 1 Comments: 0

Pg 1435 Pg 1436 Pg 1437 Pg 1438 Pg 1439 Pg 1440 Pg 1441 Pg 1442 Pg 1443 Pg 1444

Contact: info@tinkutara.com