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AllQuestion and Answers: Page 1407

Question Number 68062 Answers: 0 Comments: 1

Question Number 68052 Answers: 0 Comments: 0

Question Number 68046 Answers: 1 Comments: 0

Question Number 68041 Answers: 0 Comments: 1

Question Number 68040 Answers: 1 Comments: 2

find f(a) =∫_1 ^2 arctan(x+(a/x))dx and calculate f^′ (a) at form of integral

$${find}\:{f}\left({a}\right)\:=\int_{\mathrm{1}} ^{\mathrm{2}} {arctan}\left({x}+\frac{{a}}{{x}}\right){dx}\:\:{and} \\ $$$${calculate}\:{f}^{'} \left({a}\right)\:{at}\:{form}\:{of}\:{integral} \\ $$

Question Number 68039 Answers: 0 Comments: 1

find ∫ arctan(x+(1/x))dx

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

Question Number 68038 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((arctan(x^2 −1))/(x^2 +4))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} −\mathrm{1}\right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}{dx} \\ $$

Question Number 68037 Answers: 1 Comments: 0

find ∫ ((x^2 dx)/((x^3 −8)(x^4 +1)))

$${find}\:\int\:\:\:\frac{{x}^{\mathrm{2}} {dx}}{\left({x}^{\mathrm{3}} −\mathrm{8}\right)\left({x}^{\mathrm{4}} \:+\mathrm{1}\right)} \\ $$

Question Number 68036 Answers: 0 Comments: 1

let f(x) =cos(αx) ,2π periodic developp f at fourier serie. α ∈ R−Z

$${let}\:{f}\left({x}\right)\:={cos}\left(\alpha{x}\right)\:\:,\mathrm{2}\pi\:{periodic}\:\:\:{developp}\:{f}\:{at}\:{fourier}\:{serie}. \\ $$$$\alpha\:\in\:{R}−{Z} \\ $$

Question Number 68035 Answers: 0 Comments: 4

let f(x) =e^(−iαx) ,2π periodic .developp f at fourier serie.

$${let}\:{f}\left({x}\right)\:={e}^{−{i}\alpha{x}} \:\:\:\:,\mathrm{2}\pi\:\:{periodic}\:\:.{developp}\:{f}\:{at}\:{fourier}\:{serie}. \\ $$

Question Number 68034 Answers: 0 Comments: 1

let f(x) =e^(−x) , 2π periodic developp f at fourier serie.

$${let}\:{f}\left({x}\right)\:={e}^{−{x}} \:\:,\:\:\mathrm{2}\pi\:\:{periodic}\:\:{developp}\:{f}\:{at}\:{fourier}\:{serie}. \\ $$

Question Number 68033 Answers: 1 Comments: 0

find ∫ (dx/(1+sinx +sin(2x)))

$${find}\:\int\:\:\frac{{dx}}{\mathrm{1}+{sinx}\:+{sin}\left(\mathrm{2}{x}\right)} \\ $$

Question Number 68028 Answers: 0 Comments: 0

Question Number 68022 Answers: 1 Comments: 1

Question Number 68021 Answers: 1 Comments: 1

Question Number 68019 Answers: 0 Comments: 5

let F(x) =∫_x ^(x^2 +1) e^(−2t) sin(xt)dt determine F^′ (x) and calculate lim_(x→0) F(x).

$${let}\:{F}\left({x}\right)\:=\int_{{x}} ^{{x}^{\mathrm{2}} +\mathrm{1}} {e}^{−\mathrm{2}{t}} {sin}\left({xt}\right){dt} \\ $$$${determine}\:{F}\:^{'} \left({x}\right)\:{and}\:{calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:{F}\left({x}\right). \\ $$$$ \\ $$

Question Number 68001 Answers: 0 Comments: 1

let F(x)=∫_(2x) ^(x^2 +1) (e^(−xt) /(x+2t))dt calculate F^′ (x)

$${let}\:{F}\left({x}\right)=\int_{\mathrm{2}{x}} ^{{x}^{\mathrm{2}} +\mathrm{1}} \:\:\frac{{e}^{−{xt}} }{{x}+\mathrm{2}{t}}{dt}\:\:\:\:{calculate}\:{F}\:^{'} \left({x}\right) \\ $$

Question Number 67997 Answers: 0 Comments: 0

5y^2 +2axy+b=0 ay^2 +2bx+5c=0 (5x+3a)y^2 +(4ax^2 )y−bx−5c=0 5y^2 −x(5x+2a)y−ax^3 −3b=0 Please solve simultaneously for x and y such that all four equations are obeyed.

$$\mathrm{5}{y}^{\mathrm{2}} +\mathrm{2}{axy}+{b}=\mathrm{0} \\ $$$${ay}^{\mathrm{2}} +\mathrm{2}{bx}+\mathrm{5}{c}=\mathrm{0} \\ $$$$\left(\mathrm{5}{x}+\mathrm{3}{a}\right){y}^{\mathrm{2}} +\left(\mathrm{4}{ax}^{\mathrm{2}} \right){y}−{bx}−\mathrm{5}{c}=\mathrm{0} \\ $$$$\mathrm{5}{y}^{\mathrm{2}} −{x}\left(\mathrm{5}{x}+\mathrm{2}{a}\right){y}−{ax}^{\mathrm{3}} −\mathrm{3}{b}=\mathrm{0} \\ $$$${Please}\:{solve}\:{simultaneously} \\ $$$${for}\:{x}\:{and}\:{y}\:{such}\:{that}\:{all}\:{four} \\ $$$${equations}\:{are}\:{obeyed}. \\ $$

Question Number 67996 Answers: 1 Comments: 4

Question Number 67992 Answers: 1 Comments: 0

(1) z=a+bi (2) z=re^(iθ) express the values of (a) real (z^z ) [real part] (b) imag (z^z ) [imaginary part] (c) abs (z^z ) [absolute value] (d) arg (z^z ) [argument = angle]

$$\left(\mathrm{1}\right)\:{z}={a}+{b}\mathrm{i} \\ $$$$\left(\mathrm{2}\right)\:{z}={r}\mathrm{e}^{\mathrm{i}\theta} \\ $$$$\mathrm{express}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{real}\:\left({z}^{{z}} \right)\:\:\:\:\:\left[\mathrm{real}\:\mathrm{part}\right] \\ $$$$\left(\mathrm{b}\right)\:\mathrm{imag}\:\left({z}^{{z}} \right)\:\:\:\:\:\left[\mathrm{imaginary}\:\mathrm{part}\right] \\ $$$$\left(\mathrm{c}\right)\:\mathrm{abs}\:\left({z}^{{z}} \right)\:\:\:\:\:\left[\mathrm{absolute}\:\mathrm{value}\right] \\ $$$$\left(\mathrm{d}\right)\:\mathrm{arg}\:\left({z}^{{z}} \right)\:\:\:\:\:\left[\mathrm{argument}\:=\:\mathrm{angle}\right] \\ $$

Question Number 67991 Answers: 1 Comments: 1

Question Number 67983 Answers: 2 Comments: 1

Question Number 67977 Answers: 1 Comments: 1

Question Number 67974 Answers: 0 Comments: 2

let F(x) =∫_x ^x^2 ((arctan(xt))/(x^2 +t^2 ))dt calculate F^′ (x).

$${let}\:{F}\left({x}\right)\:=\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\:\frac{{arctan}\left({xt}\right)}{{x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} }{dt}\:\:{calculate}\:{F}\:^{'} \left({x}\right). \\ $$

Question Number 67973 Answers: 0 Comments: 5

Question Number 67972 Answers: 2 Comments: 0

if F(x)=∫_(u(x)) ^(v(x)) g(x,t)dt determine a expression for F^′ (x).

$${if}\:{F}\left({x}\right)=\int_{{u}\left({x}\right)} ^{{v}\left({x}\right)} {g}\left({x},{t}\right){dt}\:\:\:\:\:{determine}\:{a}\:{expression}\:{for}\:{F}\:^{'} \left({x}\right). \\ $$

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