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Question Number 29848 Answers: 0 Comments: 1

find Σ_(k=0) ^n cos(kx) and Σ_(k=0) ^n sin(kx) .

$f i n d \sum_{k = 0}^{n} c o s (k x) a n d \sum_{k = 0}^{n} s i n (k x) .$

Question Number 29847 Answers: 0 Comments: 0

θ ∈]0,π[ find he values of Σ_(n=1) ^∞ (1/n)cos(nθ) and Σ_(n=1) ^∞ (1/n)sin(nθ) .

$θ \in] 0, π [f i n d h e v a l u e s o f \sum_{n = 1}^{\infty} \frac{1}{n} c o s (n θ) a n d$ $\sum_{n = 1}^{\infty} \frac{1}{n} s i n (n θ) .$

Question Number 29846 Answers: 0 Comments: 1

give the developpement at integr series for f(x)=((ln(1+x)−ln(1−x))/x) 2)find lim_(x→0) f(x).

$g i v e t h e d e v e l o p p e m e n t a t i n t e g r s e r i e s f o r$ $f (x) = \frac{l n (1 + x) - l n (1 - x)}{x}$ $2) f i n d {l i m}_{x \to 0} f (x) .$

Question Number 29845 Answers: 0 Comments: 2

find lim_(x→0) ((tanx −x−(1/3)x^3 )/x^5 ) .

$f i n d {l i m}_{x \to 0} \frac{t a n x - x - \frac{1}{3} x^{3}}{x^{5}} .$

Question Number 29844 Answers: 0 Comments: 0

let give f_α (t)=cos(αt) 2π periodic with t ∈[−π,π]and α∈ R−Z 1) developp f_α at fourier serie and prove that cotan(απ)= (1/(απ)) +Σ_(n=1) ^∞ ((2α)/(π(α^2 −n^2 ))) 2)let x∈]0,π[ ant g(t)=cotant −(1/t) if t∈]0,x]andg(0)=0 prove that g is continue in[0,x] and find ∫_0 ^x g(t)dt 3)prove that ∀ t∈[0,x] g(t)=2t Σ_(n=1) ^∞ (1/(t^2 −n^2 π^(24) )) 4) chow that Π_(n=1) ^∞ (1−(x^2 /(n^2 π^2 )))= ((sinx)/x) and for x∈]−π,π[ sinx=x Π_(n=1) ^∞ (1−(x^2 /(n^2 π^2 ))) .

$l e t g i v e f_{α} (t) = c o s (α t) 2 π p e r i o d i c w i t h t \in [- π, π] a n d$ $α \in R - Z$ $1) d e v e l o p p f_{α} a t f o u r i e r s e r i e a n d p r o v e t h a t$ $c o t a n (α π) = \frac{1}{α π} + \sum_{n = 1}^{\infty} \frac{2 α}{π (α^{2} - n^{2})}$ $2) l e t x \in] 0, π [a n t g (t) = c o t a n t - \frac{1}{t} i f t \in] 0, x] a n d g (0) = 0$ $p r o v e t h a t g i s c o n t i n u e i n [0, x] a n d f i n d \int_{0}^{x} g (t) d t$ $3) p r o v e t h a t \forall t \in [0, x] g (t) = 2 t \sum_{n = 1}^{\infty} \frac{1}{t^{2} - n^{2} π^{24}}$ $4) c h o w t h a t \prod_{n = 1}^{\infty} (1 - \frac{x^{2}}{n^{2} π^{2}}) = \frac{s i n x}{x} a n d f o r x \in] - π, π [$ $s i n x = x \prod_{n = 1}^{\infty} (1 - \frac{x^{2}}{n^{2} π^{2}}) .$

Question Number 29842 Answers: 0 Comments: 1

prove that ∀ x∈]0,1[ (1/(Γ(x).Γ(1−x)))=x Π_(n=1) ^∞ (1−(x^2 /n^2 )).

$p r o v e t h a t \forall x \in] 0, 1 [\frac{1}{Γ (x) . Γ (1 - x)} = x \prod_{n = 1}^{\infty} (1 - \frac{x^{2}}{n^{2}}) .$

Question Number 29841 Answers: 0 Comments: 0

prove that ∀ x∈]0,1[ Γ(x).Γ(1−x)= (π/(sin(πx))) (compliments formula).

$p r o v e t h a t \forall x \in] 0, 1 [Γ (x) . Γ (1 - x) = \frac{π}{s i n (π x)}$ $(c o m p l i m e n t s f o r m u l a) .$

Question Number 29885 Answers: 1 Comments: 2

∫(1/(1+sinx))dx=?

$\int \frac{1}{1 + \sin x} d x = ?$

Question Number 29839 Answers: 0 Comments: 0

find Π_(n=1) ^∞ (1−(x^2 /(n^2 π^2 ))).

$f i n d \prod_{n = 1}^{\infty} (1 - \frac{x^{2}}{n^{2} π^{2}}) .$

Question Number 29838 Answers: 0 Comments: 0

find Π_(n=1) ^∞ (1−(1/(4n^2 ))).

$f i n d \prod_{n = 1}^{\infty} (1 - \frac{1}{4 n^{2}}) .$

Question Number 29837 Answers: 0 Comments: 0

let give T_n (x)=cos(n arcosx) with x∈[−1,1] 1) prove that T_n is a polynomial and T_n ∈Z[x] 2)calculate T_1 , T_2 , T_3 ,and T_4 3) prove that T_(n+2) (x)=2x T_(n+1) (x)−T_n (x) 4)find the roots of T_n and factorize T_n (x).

$l e t g i v e T_{n} (x) = c o s (n a r c o s x) w i t h x \in [- 1, 1]$ $1) p r o v e t h a t T_{n} i s a p o l y n o m i a l a n d T_{n} \in Z [x]$ $2) c a l c u l a t e T_{1}, T_{2}, T_{3}, a n d T_{4}$ $3) p r o v e t h a t T_{n + 2} (x) = 2 x T_{n + 1} (x) - T_{n} (x)$ $4) f i n d t h e r o o t s o f T_{n} a n d f a c t o r i z e T_{n} (x) .$

Question Number 29836 Answers: 0 Comments: 0

let give u_n = Σ_(q=1) ^n (1/(n^2 +q)) find lim_(n→+∞) (1−nu_n )n.

$l e t g i v e u_{n} = \sum_{q = 1}^{n} \frac{1}{n^{2} + q} f i n d {l i m}_{n \to + \infty} (1 - {n u}_{n}) n .$

Question Number 29835 Answers: 0 Comments: 0

let give f(x)=−x +2 +((√(x+1))/x) 1) study the variation of and give the graph C_f 2)give the equation of tangent at C_f in point A(1,f(1))

$l e t g i v e f (x) = - x + 2 + \frac{\sqrt{x + 1}}{x}$ $1) s t u d y t h e v a r i a t i o n o f a n d g i v e t h e g r a p h C_{f}$ $2) g i v e t h e e q u a t i o n o f t a n g e n t a t C_{f} i n p o i n t A (1, f (1))$

Question Number 29834 Answers: 0 Comments: 1

find (1/(cos^4 ((π/9)))) +(1/(cos^4 (((3π)/9)))) + (1/(cos^4 (((5π)/9)))) +(1/(cos^4 (((7π)/9)))) .

$f i n d \frac{1}{{c o s}^{4} (\frac{π}{9})} + \frac{1}{{c o s}^{4} (\frac{3 π}{9})} + \frac{1}{{c o s}^{4} (\frac{5 π}{9})} + \frac{1}{{c o s}^{4} (\frac{7 π}{9})} .$

Question Number 29833 Answers: 1 Comments: 0

find cos^4 ((π/8)) +cos^4 (((3π)/8)) +cos^4 (((5π)/8)) +cos^4 (((7π)/8)).

$f i n d {c o s}^{4} (\frac{π}{8}) + {c o s}^{4} (\frac{3 π}{8}) + {c o s}^{4} (\frac{5 π}{8}) + {c o s}^{4} (\frac{7 π}{8}) .$

Question Number 29832 Answers: 0 Comments: 0

p is a polynomial having n roots x_i with x_i ≠x_j for i≠j prove that Σ_(i=1) ^n ((p^(′′) (x_i ))/(p^′ (x_i )))=0

$p i s a p o l y n o m i a l h a v i n g n r o o t s x_{i} w i t h x_{i} \neq x_{j} f o r i \neq j$ $p r o v e t h a t \sum_{i = 1}^{n} \frac{p^{^{″}} (x_{i})}{p^{^{'}} (x_{i})} = 0$

Question Number 29821 Answers: 1 Comments: 3

((sin 16x)/(sin x)) ?pls help.

$\frac{\sin 16 x}{\sin x} ? pls help .$

Question Number 29820 Answers: 1 Comments: 3

Question Number 29805 Answers: 0 Comments: 1

f(x)=(x+a_1 )(x+a_2 )(x+a_3 )...(x+a_n ) find the coefficient of term x^k (0≤k≤n)

$f (x) = (x + a_{1}) (x + a_{2}) (x + a_{3}) . . . (x + a_{n})$ $f i n d t h e c o e f f i c i e n t o f t e r m x^{k} (0 ⩽ k ⩽ n)$

Question Number 29818 Answers: 1 Comments: 0

4, 8, 16, 31, 57, 99, 163, T_8 ,T_9 , .... Find T_8 , T_9 .

$4, 8, 16, 31, 57, 99, 163, T_{8}, T_{9}, . . . .$ $F i n d T_{8}, T_{9} .$

Question Number 29794 Answers: 0 Comments: 9

Fluids:

$F l u i d s :$

Question Number 29831 Answers: 0 Comments: 0

let give f(x)= (1/(1+x^2 )) 1)prove that prove that f^((n)) (x)=((p_n (x))/((1+x^2 )^(n+1) )) with p_n is a polynomial 2) prove that p_(n+1) (x)=(1+x^2 )p_n ^′ (x) −2(n+1)p_n (x) 3) calculate p_0 (x) ,p_1 (x) ,p_2 (x) ,p_3 (x) .

$l e t g i v e f (x) = \frac{1}{1 + x^{2}} 1) p r o v e t h a t p r o v e t h a t$ $f^{(n)} (x) = \frac{p_{n} (x)}{{(1 + x^{2})}^{n + 1}} w i t h p_{n} i s a p o l y n o m i a l$ $2) p r o v e t h a t p_{n + 1} (x) = (1 + x^{2}) p_{n}^{^{'}} (x) - 2 (n + 1) p_{n} (x)$ $3) c a l c u l a t e p_{0} (x), p_{1} (x), p_{2} (x), p_{3} (x) .$

Question Number 29786 Answers: 0 Comments: 0

Question Number 29785 Answers: 0 Comments: 0

Question Number 29778 Answers: 1 Comments: 0

Question Number 29803 Answers: 0 Comments: 3

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