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Question Number 38740 Answers: 1 Comments: 4

find tbe polynom p withdegre 5 wich verify p(x+1)−p(x)=x^4 and p(0)=0 for that put p(x)=ax^5 +bx^4 +cx^3 +dx^2 +ex +f and find the coefficients. 2) find interms of n the value of sum 1 +2^4 +3^4 +....+n^4 .

$${find}\:{tbe}\:{polynom}\:{p}\:{withdegre}\:\mathrm{5}\:{wich}\:{verify} \\ $$$${p}\left({x}+\mathrm{1}\right)−{p}\left({x}\right)={x}^{\mathrm{4}} \:\:{and}\:{p}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${for}\:{that}\:{put}\:{p}\left({x}\right)={ax}^{\mathrm{5}} \:+{bx}^{\mathrm{4}} \:+{cx}^{\mathrm{3}} \:+{dx}^{\mathrm{2}} \\ $$$$+{ex}\:+{f}\:\:{and}\:{find}\:{the}\:{coefficients}. \\ $$$$\left.\mathrm{2}\right)\:{find}\:{interms}\:{of}\:{n}\:{the}\:{value}\:{of} \\ $$$${sum}\:\mathrm{1}\:+\mathrm{2}^{\mathrm{4}} \:+\mathrm{3}^{\mathrm{4}} +....+{n}^{\mathrm{4}} \:. \\ $$

Question Number 38734 Answers: 0 Comments: 1

Find the domain of the function f (x) = 1 − cos^2 x

$${Find}\:{the}\:{domain}\:{of}\:{the}\:{function} \\ $$$${f}\:\left({x}\right)\:=\:\mathrm{1}\:−\:{cos}^{\mathrm{2}} \:{x} \\ $$

Question Number 38731 Answers: 0 Comments: 1

Question Number 38728 Answers: 0 Comments: 1

find L ( (e^(−(x/a)) /a)) with a≠0 and L laplace transfom.

$${find}\:{L}\:\left(\:\frac{{e}^{−\frac{{x}}{{a}}} }{{a}}\right)\:\:{with}\:{a}\neq\mathrm{0}\:\:{and}\:{L}\:{laplace}\:{transfom}. \\ $$

Question Number 38727 Answers: 0 Comments: 2

let n from N and A_n = ∫_(−∞) ^(+∞) ((cos(ax))/((x^2 +x+1)^n ))dx and B_n = ∫_(−∞) ^(+∞) ((sin(ax))/((x^2 +x+1)^n ))dx find the value of A_(n ) and B_n .

$${let}\:{n}\:{from}\:{N}\:\:{and}\:\:{A}_{{n}} =\:\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{cos}\left({ax}\right)}{\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right)^{{n}} }{dx}\:\:{and} \\ $$$${B}_{{n}} =\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{sin}\left({ax}\right)}{\left({x}^{\mathrm{2}} \:+{x}+\mathrm{1}\right)^{{n}} }{dx} \\ $$$${find}\:{the}\:{value}\:{of}\:{A}_{{n}\:} \:\:{and}\:{B}_{{n}} \:\:. \\ $$$$ \\ $$

Question Number 38726 Answers: 0 Comments: 1

let f(x)=((x+1)/(2 +e^(−2x) )) developp f at integr serie.

$${let}\:{f}\left({x}\right)=\frac{{x}+\mathrm{1}}{\mathrm{2}\:+{e}^{−\mathrm{2}{x}} }\:\:\:{developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$

Question Number 38725 Answers: 0 Comments: 1

let f(x)=ln(1+ e^(−x) ) developp f at integr serie .

$${let}\:{f}\left({x}\right)={ln}\left(\mathrm{1}+\:{e}^{−{x}} \right)\:\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 38724 Answers: 0 Comments: 2

calculate ∫_0 ^∞ ((x^2 cos(πx))/((x^2 +4)^2 ))dx

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{2}} {cos}\left(\pi{x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{4}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 38723 Answers: 0 Comments: 1

find the value of ∫_0 ^∞ ((xsin(3x))/((1+x^2 )^2 ))dx

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{xsin}\left(\mathrm{3}{x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$

Question Number 38722 Answers: 0 Comments: 1

let f(x)= (x+1)e^(−x) and g(x)=ln(2+x^2 ) 1) calculate fog(x) and gof(x) 2) calculate (fog)^′ (x) and (gof)^′ (x).

$${let}\:{f}\left({x}\right)=\:\left({x}+\mathrm{1}\right){e}^{−{x}} \:\:{and}\:\:{g}\left({x}\right)={ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{fog}\left({x}\right)\:{and}\:{gof}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\left({fog}\right)^{'} \left({x}\right)\:{and}\:\left({gof}\right)^{'} \left({x}\right). \\ $$

Question Number 38721 Answers: 0 Comments: 4

let f(x)=(√(1+2x^2 )) −x(√2) +3 1) calculate lim_(x→+∞) f(x) and lim_(x→−∞) f(x) 2)calculate lim_(x→+∞) ((f(x))/x) and lim_(x→−∞) ((f(x))/x) 3)give the assymtote to graph C_f 4) give the assymtote to C_f at point A(0,f(0)) 5) find f^(−1) (x) and calculate (f^(−1) )^′ (x) 6) calculate ∫_0 ^1 f(x)dx.

$${let}\:\:{f}\left({x}\right)=\sqrt{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }\:\:−{x}\sqrt{\mathrm{2}}\:\:+\mathrm{3} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} \:{f}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow−\infty} {f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:{lim}_{{x}\rightarrow+\infty} \:\:\frac{{f}\left({x}\right)}{{x}}\:{and}\:{lim}_{{x}\rightarrow−\infty} \:\:\frac{{f}\left({x}\right)}{{x}} \\ $$$$\left.\mathrm{3}\right){give}\:{the}\:{assymtote}\:{to}\:{graph}\:{C}_{{f}} \\ $$$$\left.\mathrm{4}\right)\:{give}\:{the}\:{assymtote}\:{to}\:{C}_{{f}} \:\:{at}\:{point}\:{A}\left(\mathrm{0},{f}\left(\mathrm{0}\right)\right) \\ $$$$\left.\mathrm{5}\right)\:{find}\:{f}^{−\mathrm{1}} \left({x}\right)\:{and}\:{calculate}\:\left({f}^{−\mathrm{1}} \right)^{'} \left({x}\right) \\ $$$$\left.\mathrm{6}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx}. \\ $$

Question Number 38718 Answers: 0 Comments: 3

1) find f(x)=∫_0 ^π ln(2+x cosθ)dθ 2) calculate ∫_0 ^π ln(2 +cosθ)dθ

$$\left.\mathrm{1}\right)\:{find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\mathrm{2}+{x}\:{cos}\theta\right){d}\theta \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\mathrm{2}\:\:+{cos}\theta\right){d}\theta \\ $$$$ \\ $$

Question Number 38720 Answers: 0 Comments: 2

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

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

Question Number 38719 Answers: 1 Comments: 0

find ∫ ln((√x) +(√(x+1)))dx

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

Question Number 38716 Answers: 1 Comments: 1

calculate ∫_2 ^5 (dx/((x +1−[x])^2 ))

$${calculate}\:\:\:\int_{\mathrm{2}} ^{\mathrm{5}} \:\:\:\:\:\frac{{dx}}{\left({x}\:+\mathrm{1}−\left[{x}\right]\right)^{\mathrm{2}} } \\ $$

Question Number 38714 Answers: 1 Comments: 1

calculate ∫_1 ^6 (((−1)^([x]) )/(1+x^2 [x]))dx

$${calculate}\:\:\:\int_{\mathrm{1}} ^{\mathrm{6}} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\mathrm{1}+{x}^{\mathrm{2}} \left[{x}\right]}{dx} \\ $$

Question Number 38707 Answers: 0 Comments: 3

Question Number 38706 Answers: 0 Comments: 4

let f(x)= ∫_0 ^(π/2) (dθ/(1+x e^(iθ) )) with ∣x∣<1 1) developp f(x) at integr serie 2) calculate f(x) 3) find the value of ∫_0 ^(π/2) (e^(iθ) /((1+x e^(iθ) )^2 )) 4) calculate ∫_0 ^(π/2) (dθ/(2 +e^(iθ) ))

$${let}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\frac{{d}\theta}{\mathrm{1}+{x}\:{e}^{{i}\theta} }\:\:\:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{developp}\:{f}\left({x}\right)\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{e}^{{i}\theta} }{\left(\mathrm{1}+{x}\:{e}^{{i}\theta} \right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{d}\theta}{\mathrm{2}\:+{e}^{{i}\theta} } \\ $$

Question Number 38699 Answers: 1 Comments: 0