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Question Number 34606 Answers: 0 Comments: 0

let give p(x)=(x+1)^n −(x−1)^n 1) factorize p(x) inside C[x] 2) find the value of Π_(k=1) ^p cotan(((kπ)/(2p+1)))

$l e t g i v e p (x) = {(x + 1)}^{n} - {(x - 1)}^{n}$ $1) f a c t o r i z e p (x) i n s i d e C [x]$ $2) f i n d t h e v a l u e o f \prod_{k = 1}^{p} c o t a n (\frac{k π}{2 p + 1})$

Question Number 34605 Answers: 0 Comments: 0

decompose inside R(x) thefraction F(x)= ((x^5 +1)/(x^2^ (x−1)^2 )) .

$d e c o m p o s e i n s i d e R (x) t h e f r a c t i o n$ $F (x) = \frac{x^{5} + 1}{x^{2^{}} {(x - 1)}^{2}} .$

Question Number 34604 Answers: 0 Comments: 0

let p(x)= x^n +x+1 ∈C[x] and z∈C/p(z)=0 prove that ∣z∣<2 .

$l e t p (x) = x^{n} + x + 1 \in C [x] a n d z \in C / p (z) = 0$ $p r o v e t h a t ∣ z ∣< 2 .$

Question Number 34603 Answers: 0 Comments: 0

prove that ∀ p∈K[x] p(x) −x divide p(p(x))−x

$p r o v e t h a t \forall p \in K [x] p (x) - x d i v i d e p (p (x)) - x$

Question Number 34602 Answers: 0 Comments: 0

simplify Σ_(k=0) ^n ((k/n) −α)^2 C_n ^k x^k (1−x)^(n−k ) α∈C.

$s i m p l i f y \sum_{k = 0}^{n} {(\frac{k}{n} - α)}^{2} C_{n}^{k} x^{k} {(1 - x)}^{n - k}$ $α \in C .$

Question Number 34596 Answers: 0 Comments: 0

1) prove that Σ_(k=1) ^n H_k =(n+1)H_n −n 2) prove that Σ_(k=1) ^n H_k ^2 =(n+1)H_n ^2 −(3n+1)H_n +2n H_n =Σ_(k=1) ^n (1/k) .

$1) p r o v e t h a t \sum_{k = 1}^{n} H_{k} = (n + 1) H_{n} - n$ $2) p r o v e t h a t \sum_{k = 1}^{n} H_{k}^{2} = (n + 1) H_{n}^{2} - (3 n + 1) H_{n} + 2 n$ $H_{n} = \sum_{k = 1}^{n} \frac{1}{k} .$

Question Number 34595 Answers: 0 Comments: 0

simplify Σ_(k=1) ^n (((−1)^(k−1) )/k) C_n ^k

$s i m p l i f y \sum_{k = 1}^{n} \frac{{(- 1)}^{k - 1}}{k} C_{n}^{k}$

Question Number 34594 Answers: 0 Comments: 0

prove that Σ_(k=0) ^p (−1)^k C_n ^k =(−1)^p C_(n−1) ^p

$p r o v e t h a t \sum_{k = 0}^{p} {(- 1)}^{k} C_{n}^{k} = {(- 1)}^{p} C_{n - 1}^{p}$

Question Number 34593 Answers: 0 Comments: 0

1) calculate ∫_(−∞) ^(+∞) ((cos(αx^n ))/(x^2 +x +1)) dx with n integr natural 2) find the value of ∫_(−∞) ^∞ ((cos( α x^(2n) ))/(x^2 +x +1))dx 3) calculate ∫_(−∞) ^(+∞) ((cos(π x^3 ))/(x^2 +x +1)) dx

$1) c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{c o s (α x^{n})}{x^{2} + x + 1} d x w i t h n i n t e g r$ $n a t u r a l$ $2) f i n d t h e v a l u e o f \int_{- \infty}^{\infty} \frac{c o s (α x^{2 n})}{x^{2} + x + 1} d x$ $3) c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{c o s (π x^{3})}{x^{2} + x + 1} d x$

Question Number 34587 Answers: 2 Comments: 1

Question Number 34585 Answers: 1 Comments: 1

Question Number 34571 Answers: 0 Comments: 0

A machine with a velocity ratio of 5 requires 150J of work to raise a 500N load through a vertical distance of 200cm,calculate: a)the efficiency b)the M.A of the machine

$A m a c h i n e w i t h a v e l o c i t y r a t i o$ $o f 5 r e q u i r e s 150 J o f w o r k t o r a i s e$ $a 500 N l o a d t h r o u g h a v e r t i c a l$ $d i s t a n c e o f 200 c m, c a l c u l a t e :$ $a) t h e e f f i c i e n c y$ $b) t h e M . A o f t h e m a c h i n e$

Question Number 34567 Answers: 1 Comments: 0

x determinant ((2),())−2x−15=0

$x | \begin{matrix} 2 \end{matrix} | - 2 x - 15 = 0$

Question Number 34562 Answers: 1 Comments: 1

find the value of ∫_0 ^1 ((arctanx)/((1+x^2 )^2 )) dx

$f i n d t h e v a l u e o f \int_{0}^{1} \frac{a r c t a n x}{{(1 + x^{2})}^{2}} d x$

Question Number 34561 Answers: 0 Comments: 1

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

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

Question Number 34614 Answers: 0 Comments: 1

decompose inside R(x) the fraction F(x)= (1/((x−3)^6 (x+2))) .

$d e c o m p o s e i n s i d e R (x) t h e f r a c t i o n$ $F (x) = \frac{1}{{(x - 3)}^{6} (x + 2)} .$

Question Number 34554 Answers: 1 Comments: 3

lim_(x→∞) (((a−1+b^(1/x) )/a))^x = ? (a,b>0)

$\lim_{x \to \infty} {(\frac{a - 1 + b^{\frac{1}{x}}}{a})}^{x} = ?$ $(a, b > 0)$

Question Number 34546 Answers: 0 Comments: 0

∫(dx/(sinx+cosx+tanx+cosecx+secx+cotx))

$\int \frac{d x}{s i n x + c o s x + t a n x + c o s e c x + s e c x + c o t x}$

Question Number 34543 Answers: 0 Comments: 2

Question Number 34540 Answers: 0 Comments: 2

a) lim_(x→(π/4)) (((cos x+sin x)^3 −2(√2))/(1−sin 2x)) =? b) lim_(x→0) (sin x)^(1/x) = ?

$a) \lim_{x \to \frac{π}{4}} \frac{{(\cos x + \sin x)}^{3} - 2 \sqrt{2}}{1 - \sin 2 x} = ?$ $b) \lim_{x \to 0} {(\sin x)}^{\frac{1}{x}} = ?$

Question Number 34533 Answers: 2 Comments: 5

Solve for x : 5 log_4 x + 48 log_x 4 = (x/8)

$Solve for x : 5 \log_{4} x + 48 \log_{x} 4 = \frac{x}{8}$

Question Number 34528 Answers: 1 Comments: 1

Find radius c in terms of radii a and b.

$F i n d r a d i u s c i n t e r m s o f r a d i i$ $a a n d b .$

Question Number 34522 Answers: 0 Comments: 2

lim_(x→0) log _e {((sin (a+(1/x)))/(sin a))}^x , 0<a<(π/2) .

$\lim_{x \to 0} \log_{e} {\frac{\sin (a + \frac{1}{x})}{\sin a}}^{x}, 0 < a < \frac{π}{2} .$

Question Number 34516 Answers: 2 Comments: 1

lim_(x→0) log _(tan^2 x) (tan^2 2x) = ?

$\lim_{x \to 0} \log_{\tan^{2} x} (\tan^{2} 2 x) = ?$

Question Number 34504 Answers: 1 Comments: 1

1−(1/2)+(1/3)−(1/5)+.... find the sum of the series

$1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{5} + . . . .$ $f i n d t h e s u m o f t h e s e r i e s$

Question Number 34501 Answers: 1 Comments: 1

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