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AllQuestion and Answers: Page 1441

Question Number 61767 Answers: 0 Comments: 0

Question Number 61762 Answers: 2 Comments: 1

Question Number 61755 Answers: 1 Comments: 2

if f(z)=Σ_(k=1) ^n a_k z^k ,a_k ,z∈C.Prove a_k =(1/(2πi))∫_(∣z∣=r ) ((f(z))/z^(k+1) )dz

$if f (z) = \underset{k = 1}{\sum^{n}} a_{k} z^{k}, a_{k}, z \in C . Prove$ $a_{k} = \frac{1}{2 π i} \int_{∣ z ∣= r} \frac{f (z)}{z^{k + 1}} d z$

Question Number 61754 Answers: 0 Comments: 0

Question Number 61748 Answers: 0 Comments: 1

find ∫ (dx/(sin(2x)+tan(x)))dx

$f i n d \int \frac{d x}{s i n (2 x) + t a n (x)} d x$

Question Number 61752 Answers: 0 Comments: 0

solve the (de) (√(2x+1))y^′ −x^3 y = xln(x)

$s o l v e t h e (d e) \sqrt{2 x + 1} y^{^{'}} - x^{3} y = x l n (x)$

Question Number 61751 Answers: 0 Comments: 0

use newton method to solve the equation x^4 −3x−1 =0

$u s e n e w t o n m e t h o d t o s o l v e t h e e q u a t i o n x^{4} - 3 x - 1 = 0$

Question Number 61750 Answers: 0 Comments: 0

find ∫ ((x^2 −(√(x−1)))/(2(√(x^2 +3)))) dx

$f i n d \int \frac{x^{2} - \sqrt{x - 1}}{2 \sqrt{x^{2} + 3}} d x$

Question Number 61749 Answers: 0 Comments: 0

find ∫ (dx/(cos(2x)+tan(x)))

$f i n d \int \frac{d x}{c o s (2 x) + t a n (x)}$

Question Number 61744 Answers: 0 Comments: 7

3xy^2 +x^3 =9 −−−−−(1) 3x^2 y+y^3 =18−−−−(2) Find x and y

$3 {x y}^{2} + x^{3} = 9 - - - - - (1)$ $3 x^{2} y + y^{3} = 18 - - - - (2)$ $F i n d x a n d y$

Question Number 61738 Answers: 2 Comments: 0

Question Number 61735 Answers: 0 Comments: 0

∫_(−1) ^1 (((sin(x))/(sinh^(−1) (x))))(((sin^(−1) (x))/(sinh(x)))) dx =?

$\underset{- 1}{\int^{1}} (\frac{s i n (x)}{{s i n h}^{- 1} (x)}) (\frac{{s i n}^{- 1} (x)}{s i n h (x)}) d x = ?$

Question Number 61733 Answers: 0 Comments: 1

Find the maximum volume tetrahedron inside an ellipsoid, parameters a,b,c .

$F i n d t h e m a x i m u m$ $v o l u m e t e t r a h e d r o n i n s i d e a n$ $e l l i p s o i d, p a r a m e t e r s a, b, c .$

Question Number 61721 Answers: 0 Comments: 0

calculate A =∫_0 ^∞ cos(x^n )dx and B =∫_0 ^∞ sin(x^n )dx with n≥2 (n integr natural)

$c a l c u l a t e A = \int_{0}^{\infty} c o s (x^{n}) d x$ $a n d B = \int_{0}^{\infty} s i n (x^{n}) d x w i t h$ $n ⩾ 2 (n i n t e g r n a t u r a l)$

Question Number 61719 Answers: 0 Comments: 1

∫(dx/(2+sin(x)))

$\int \frac{d x}{2 + s i n (x)}$

Question Number 61708 Answers: 0 Comments: 1

8+(4+3×2)

$8 + (4 + 3 \times 2)$

Question Number 61707 Answers: 0 Comments: 1

6^(−3)

$6^{- 3}$

Question Number 61706 Answers: 0 Comments: 1

(7^(10) /7^7 )

$\frac{7^{10}}{7^{7}}$

Question Number 61694 Answers: 1 Comments: 1

Question Number 61692 Answers: 0 Comments: 0

if(3/2)≤x≤5, prove:2(√(x+1))+(√(2x−3))+(√(15−3x))<2(√(19))

$i f \frac{3}{2} ⩽ x ⩽ 5,$ $p r o v e : 2 \sqrt{x + 1} + \sqrt{2 x - 3} + \sqrt{15 - 3 x} < 2 \sqrt{19}$

Question Number 61691 Answers: 0 Comments: 0

f(x)=(√(x^4 −3x^2 +4))+(√(x^4 −3x^2 −8x+20)) find the minimum value of f(x)

$f (x) = \sqrt{x^{4} - 3 x^{2} + 4} + \sqrt{x^{4} - 3 x^{2} - 8 x + 20}$ $f i n d t h e m i n i m u m v a l u e o f f (x)$

Question Number 61700 Answers: 1 Comments: 0

Question Number 61724 Answers: 0 Comments: 6

Σ_(n≥0) n^2 x^n

$\sum_{n ⩾ 0} n^{2} x^{n}$

Question Number 61662 Answers: 0 Comments: 1

calculate ∫_(−(π/4)) ^(π/4) ((cosx)/(e^(1/x) +1)) dx

$c a l c u l a t e \int_{- \frac{π}{4}}^{\frac{π}{4}} \frac{c o s x}{e^{\frac{1}{x}} + 1} d x$

Question Number 61661 Answers: 0 Comments: 1

1) calculate ∫∫_R^+^2 ((dxdy)/((1+x^2 )(1+y^2 ))) 2) find the value of ∫_0 ^∞ ((ln(x))/(x^2 −1)) dx .

$1) c a l c u l a t e \int \int_{R^{+^{2}}} \frac{d x d y}{(1 + x^{2}) (1 + y^{2})}$ $2) f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{l n (x)}{x^{2} - 1} d x .$

Question Number 61660 Answers: 0 Comments: 1

let U_n = ∫_0 ^∞ (dt/((1+t^3 )^n )) dt (n≥1) 1) calculate (U_(n+1) /U_n ) 2) study the serie Σln((U_(n+1) /U_n )) and prove that lim_(n→+∞) U_n =0

$l e t U_{n} = \int_{0}^{\infty} \frac{d t}{{(1 + t^{3})}^{n}} d t (n ⩾ 1)$ $1) c a l c u l a t e \frac{U_{n + 1}}{U_{n}}$ $2) s t u d y t h e s e r i e Σ l n (\frac{U_{n + 1}}{U_{n}}) a n d p r o v e t h a t {l i m}_{n \to + \infty} U_{n} = 0$

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