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Relation and FunctionsQuestion and Answers: Page 8

Question Number 147687 Answers: 2 Comments: 0

calculate lim_(n→0) ((e^(−nx^2 ) −nx−1)/x^3 )

$calculate \lim_{n \to 0} \frac{e^{- {nx}^{2}} - nx - 1}{x^{3}}$

Question Number 147685 Answers: 2 Comments: 0

calculate lim_(x→0) ((sin(2sinx))/x^2 )

$calculate \lim_{x \to 0} \frac{\sin (2 sinx)}{x^{2}}$

Question Number 147684 Answers: 0 Comments: 0

decompse F(x)=(x^3 /((x^2 +1)^4 )) inside C(x)

$decompse F (x) = \frac{x^{3}}{{(x^{2} + 1)}^{4}} inside C (x)$

Question Number 147678 Answers: 0 Comments: 0

roots of Υ_n (x)=sin(narcsinx) (n integr natural) deompose F(x)=(1/(Υ_n (x)))

$roots of Υ_{n} (x) = \sin (narcsinx) (n integr natural)$ $deompose F (x) = \frac{1}{Υ_{n} (x)}$

Question Number 147543 Answers: 2 Comments: 0

Π_(m=1) ^n ((1/2))^m

$\underset{m = 1}{\prod^{n}} {(\frac{1}{2})}^{m}$

Question Number 147469 Answers: 0 Comments: 1

Question Number 147467 Answers: 3 Comments: 0

f(x)=x^n e^(−x) 1) calculate f^((n)) (0) and f^((n)) (1) 2)developp f at integr serie 3) calculate ∫_0 ^1 f(x)dx

$f (x) = x^{n} e^{- x}$ $1) calculate f^{(n)} (0) and f^{(n)} (1)$ $2) developp f at integr serie$ $3) calculate \int_{0}^{1} f (x) dx$

Question Number 147466 Answers: 2 Comments: 0

f(x)=x^2 −2x+5 find ∫ ((f(x))/(f^(−1) (x)))dx and ∫ ((f^(−1) (x))/(f(x)))dx

$f (x) = x^{2} - 2 x + 5$ $find \int \frac{f (x)}{f^{- 1} (x)} dx and \int \frac{f^{- 1} (x)}{f (x)} dx$

Question Number 147302 Answers: 1 Comments: 0

P_a (z)=z^(2n) −2z^n cosa+1 montrer que p_a (z)=Π_(k=0) ^(n−1) (z^2 −2zcos((a/π)+((2kπ)/n))+1)

$P_{a} (z) = z^{2 n} - 2 z^{n} c o s a + 1$ $m o n t r e r q u e p_{a} (z) = \underset{k = 0}{\prod^{n - 1}} (z^{2} - 2 z c o s (\frac{a}{π} + \frac{2 k π}{n}) + 1)$

Question Number 147258 Answers: 0 Comments: 0

Question Number 147218 Answers: 0 Comments: 0

calculate ∫_(∣z−1∣=2) (e^z /((z+i(√2))^2 (z+i)^2 (2z−1)))dz

$calculate \int_{∣ z - 1 ∣= 2} \frac{e^{z}}{{(z + i \sqrt{2})}^{2} {(z + i)}^{2} (2 z - 1)} dz$

Question Number 147205 Answers: 1 Comments: 0

calculate ∫_1 ^∞ ((arctan((3/x)))/(2x^2 +1))dx

$calculate \int_{1}^{\infty} \frac{\arctan (\frac{3}{x})}{{2 x}^{2} + 1} dx$

Question Number 147204 Answers: 0 Comments: 0

find ∫_0 ^1 lnxln(1−x)ln(1−x^2 )dx

$find \int_{0}^{1} lnxln (1 - x) \ln (1 - x^{2}) dx$

Question Number 147201 Answers: 0 Comments: 0

f(x)=cos(sinx) developp f at fourier serie

$f (x) = \cos (sinx) developp f at fourier serie$

Question Number 147100 Answers: 0 Comments: 0

findA_n = ∫_0 ^1 x(x+1)(x+2)....(x+n)dx

${findA}_{n} = \int_{0}^{1} x (x + 1) (x + 2) . . . . (x + n) dx$

Question Number 147006 Answers: 1 Comments: 0

find I_n =∫_0 ^∞ (dx/((x^2 +1)(x^2 +2)......(x^2 +n)))

$find I_{n} = \int_{0}^{\infty} \frac{dx}{(x^{2} + 1) (x^{2} + 2) . . . . . . (x^{2} + n)}$

Question Number 146902 Answers: 1 Comments: 0

let α and β roots of z^2 +3z+5=0 simlify U_n = Σ_(k=0) ^n (α^k +β^k ) and V_n =Σ_(k=0) ^n ((1/α^k )+(1/β^k ))

$let α and β roots of z^{2} + 3 z + 5 = 0$ $simlify U_{n} = \sum_{k = 0}^{n} (α^{k} + β^{k})$ $and V_{n} = \sum_{k = 0}^{n} (\frac{1}{α^{k}} + \frac{1}{β^{k}})$

Question Number 146901 Answers: 1 Comments: 0

g(x)=cos(2arcsinx) calculate (dg/dx) and (d^2 g/dx^2 ) 2)find ∫_(−(1/2)) ^(1/2) g(x)dx

$g (x) = \cos (2 arcsinx)$ $calculate \frac{dg}{dx} and \frac{d^{2} g}{{dx}^{2}}$ $2) find \int_{- \frac{1}{2}}^{\frac{1}{2}} g (x) dx$

Question Number 146899 Answers: 1 Comments: 0

f(x)=sin^5 x calculate f^((5)) ((π/2))

$f (x) = \sin^{5} x calculate f^{(5)} (\frac{π}{2})$

Question Number 146898 Answers: 2 Comments: 0

calculate ∫_0 ^∞ ((cosx)/((x^2 +1)(x^2 +2)(x^2 +3)))dx

$calculate \int_{0}^{\infty} \frac{cosx}{(x^{2} + 1) (x^{2} + 2) (x^{2} + 3)} dx$

Question Number 146705 Answers: 1 Comments: 0

find lim_(x→0) ((sin(tan(2x)−x)+1−cos(πx^2 ))/x^2 )

$find \lim_{x \to 0} \frac{\sin (\tan (2 x) - x) + 1 - \cos (π x^{2})}{x^{2}}$

Question Number 146550 Answers: 0 Comments: 0

f(x)=x^3 arctan((2/x)) 1)calculate f^((n)) (x) 2)developp f at integr srie at x_0 =1

$f (x) = x^{3} \arctan (\frac{2}{x})$ $1) calculate f^{(n)} (x)$ $2) developp f at integr srie at x_{0} = 1$

Question Number 146549 Answers: 2 Comments: 0

find lim_(x→0) ((cos(x−sinx)+1−cos(x^2 ))/x^2 )

$find \lim_{x \to 0} \frac{\cos (x - sinx) + 1 - \cos (x^{2})}{x^{2}}$

Question Number 146548 Answers: 2 Comments: 0

let f(x)=cos(αx) developp f at fourier serie (α real)

$let f (x) = \cos (α x) developp f at fourier serie (α real)$

Question Number 146547 Answers: 3 Comments: 0

calculate ∫_(∣z∣=5) ((2−z^2 )/((z^2 +9)(z−i)^2 ))dz

$calculate \int_{∣ z ∣= 5} \frac{2 - z^{2}}{(z^{2} + 9) {(z - i)}^{2}} dz$

Question Number 146546 Answers: 2 Comments: 0

find ∫_(∣z−1∣=3) ((cos(πz))/((z−2)(z^2 +4)))dz

$find \int_{∣ z - 1 ∣= 3} \frac{\cos (π z)}{(z - 2) (z^{2} + 4)} dz$

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