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Question Number 71235 Answers: 2 Comments: 1

sinh[ln (x + (√(1 + x^2 ))) ] ≡ A. 2x B. (1/x) C. x^2 D. x

$s i n h [l n (x + \sqrt{1 + x^{2}})] \equiv$ $A . 2 x$ $B . \frac{1}{x}$ $C . x^{2}$ $D . x$

Question Number 70914 Answers: 2 Comments: 3

1+(z+2i)+(z+2i)^2 +(z+2i)^3 +(z+2i)^4 =0 find z , z∈C

$1 + (z + 2 i) + {(z + 2 i)}^{2} + {(z + 2 i)}^{3} + {(z + 2 i)}^{4} = 0$ $find z, z \in C$

Question Number 70397 Answers: 0 Comments: 1

Question Number 70310 Answers: 3 Comments: 1

please help me find the term independent of x in the expansion of (x + (3/x))^(−12 )

$p l e a s e h e l p m e f i n d t h e t e r m i n d e p e n d e n t o f x$ $i n t h e e x p a n s i o n o f$ ${(x + \frac{3}{x})}^{- 12}$

Question Number 70132 Answers: 1 Comments: 1

Σ_(n=1) ^(3050) i^n

$\underset{n = 1}{\sum^{3050}} i^{n}$

Question Number 70069 Answers: 1 Comments: 2

Π_(n=1) ^5 (((12n−2)^4 +18^2 )/((12n−8)^4 +18^2 )) =(((10^4 +324)(22^4 +324)(34^4 +324)(46^4 +324)(58^4 +324))/((4^4 +324)(16^4 +324)(28^4 +324)(40^4 +324)(52^4 +324)))

$\underset{n = 1}{\prod^{5}} \frac{{(12 n - 2)}^{4} + 18^{2}}{{(12 n - 8)}^{4} + 18^{2}}$ $= \frac{(10^{4} + 324) (22^{4} + 324) (34^{4} + 324) (46^{4} + 324) (58^{4} + 324)}{(4^{4} + 324) (16^{4} + 324) (28^{4} + 324) (40^{4} + 324) (52^{4} + 324)}$

Question Number 70035 Answers: 0 Comments: 4

Question Number 70030 Answers: 1 Comments: 0

Find the convergence of Σ_(n=1) ^∞ (((1/n) + 1)/(−n^2 ))

$Find the convergence of$ $\underset{n = 1}{\sum^{\infty}} \frac{\frac{1}{n} + 1}{- n^{2}}$

Question Number 70051 Answers: 2 Comments: 0

((a+b)/c)=((cos(((a−b)/2)))/(cos(c/2)))

$\frac{a + b}{c} = \frac{c o s (\frac{a - b}{2})}{c o s \frac{c}{2}}$

Question Number 70022 Answers: 0 Comments: 1

Find all pairs of (p, q) integer(s) such that p^3 − q^5 = (p + q)^2

$F i n d a l l p a i r s o f (p, q) i n t e g e r (s) s u c h t h a t$ $p^{3} - q^{5} = {(p + q)}^{2}$

Question Number 70017 Answers: 0 Comments: 2

Solution- log_8 x+log_4 x+log_2 x=11 ⇒(1/(log_x 8))+(1/(log_x 4))+(1/(log_x 2))=11 ⇒(1/(log_x 2^3 ))+(1/(log_x 2^2 ))+(1/(log_x 2))=11 ⇒(1/(3log_x 2))+(1/(2log_x 2))+(1/(log_x 2))=11 ⇒((1/3)+(1/2)+1)(1/(log_x 2))=11 ⇒((11)/6)×(1/(log_x 2))=11 ⇒(1/(log_x 2))=11×(6/(11)) ⇒log_2 x=6 ⇒x=2^6 ∴x=64 is this rule correct????

Question Number 69894 Answers: 0 Comments: 3

∫ ((2x^5 −x)/(x^3 −2))dx

$\int \frac{2 x^{5} - x}{x^{3} - 2} d x$

Question Number 69829 Answers: 2 Comments: 2

Question Number 69778 Answers: 2 Comments: 5

prove that the equation (b^2 −4ac)x^2 + 4(a + c)x −4 = 0 is always real.

$p r o v e t h a t t h e e q u a t i o n$ $(b^{2} - 4 a c) x^{2} + 4 (a + c) x - 4 = 0 i s a l w a y s r e a l .$

Question Number 69766 Answers: 0 Comments: 4

find (dy/dx) at the point (0,3) when 2x^2 y + y + 4xy^2 = 2x + 3

$f i n d \frac{d y}{d x} a t t h e p o i n t (0, 3) w h e n 2 x^{2} y + y + 4 {x y}^{2} = 2 x + 3$

Question Number 69765 Answers: 1 Comments: 0

Given that y = (√(5x^2 + 3)) , show that when x^2 = (6/5) , (d^2 y/dx^(2 ) ) = ((125)/8)

$G i v e n t h a t y = \sqrt{5 x^{2} + 3}, s h o w t h a t w h e n x^{2} = \frac{6}{5}, \frac{d^{2} y}{{d x}^{2}} = \frac{125}{8}$

Question Number 69764 Answers: 1 Comments: 1

find (dy/dx) if x = sin^2 t and y= tan t at t = (π/4)

$f i n d \frac{d y}{d x} i f x = {s i n}^{2} t a n d y = t a n t a t t = \frac{π}{4}$

Question Number 69763 Answers: 1 Comments: 2

find (dy/dx) if y = 3^x e^(2x + 1) , at x =1

$f i n d \frac{d y}{d x} i f y = 3^{x} e^{2 x + 1}, a t x = 1$

Question Number 69762 Answers: 1 Comments: 1

prove by mathematical induction, that for all positive integers n, Σ_(r=1) ^n r(r + 1) = (n/3)(n + 1)( n + 2)

$p r o v e b y m a t h e m a t i c a l i n d u c t i o n, t h a t f o r a l l p o s i t i v e i n t e g e r s n,$ $\underset{r = 1}{\sum^{n}} r (r + 1) = \frac{n}{3} (n + 1) (n + 2)$

Question Number 69715 Answers: 1 Comments: 0

∫((x^2 +1)/((x+1)^2 ))e^x dx

$\int \frac{x^{2} + 1}{{(x + 1)}^{2}} e^{x} d x$

Question Number 69576 Answers: 1 Comments: 1

∫_(−2) ^( 2) (x^3 cos(x/2)+(1/2))(√(4−x^2 ))dx

$\int_{- 2}^{2} (x^{3} c o s \frac{x}{2} + \frac{1}{2}) \sqrt{4 - x^{2}} d x$

Question Number 69459 Answers: 0 Comments: 0

Question Number 69314 Answers: 1 Comments: 1

if 5 x y 40 are in GP .find x and y

$i f 5 x y 40 a r e i n G P . f i n d x a n d y$

Question Number 69247 Answers: 0 Comments: 1

show that c∣a ⇔ −c∣a.

$s h o w t h a t$ $c ∣ a \Leftrightarrow - c ∣ a .$

Question Number 69236 Answers: 0 Comments: 0

Use Residus theorem to prove that ∀ a>0 Σ_(n=0) ^∞ (1/( n^2 +a^2 )) = (1/2)((π/(ash(πa))) −(1/a^2 )) and Σ_(n=0) ^∞ (((−1)^n )/(n^2 +a^2 )) = (1/2)((( π)/(a.th(πa))) −(1/a^2 )) Assume that we can developp in integer serie the functions f(x)=(x/(shx)) and g(x)=(x/(thx)) Give the DL_2 of f and g around zero Why can′t we use that theorem to explicit f(a)=Σ_(n=0) ^∞ (((−1)^n )/( (2n+1)^2 +a^2 )) ???

$U s e R e s i d u s t h e o r e m t o p r o v e t h a t \forall a > 0 \underset{n = 0}{\sum^{\infty}} \frac{1}{n^{2} + a^{2}} = \frac{1}{2} (\frac{π}{a s h (π a)} - \frac{1}{a^{2}})$ $a n d \underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n}}{n^{2} + a^{2}} = \frac{1}{2} (\frac{π}{a . t h (π a)} - \frac{1}{a^{2}})$ $A s s u m e t h a t w e c a n d e v e l o p p i n i n t e g e r s e r i e t h e f u n c t i o n s$ $f (x) = \frac{x}{s h x} a n d g (x) = \frac{x}{t h x}$ $G i v e t h e {D L}_{2} o f f a n d g a r o u n d z e r o$ $W h y {c a n}^{'} t w e u s e t h a t t h e o r e m t o e x p l i c i t$ $f (a) = \underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n}}{{(2 n + 1)}^{2} + a^{2}} ? ? ?$

Question Number 69207 Answers: 1 Comments: 3

help please. A river is 5m wide and flows at 3.0ms^(−1) . A man can swim at 2.0ms^(−1) in still water. if he sets off at an angle of 90° to the bank calculate a) the mans time and velocity b) his distance downstream from the starting point till when he reaches the other side of the river bank c) the actual distance he swims through the water.

$h e l p p l e a s e .$ $A r i v e r i s 5 m w i d e a n d f l o w s a t 3.0 {m s}^{- 1} . A m a n c a n s w i m a t 2.0 {m s}^{- 1}$ $i n s t i l l w a t e r . i f h e s e t s o f f a t a n a n g l e o f 90 ° t o t h e b a n k$ $c a l c u l a t e$ $a) t h e m a n s t i m e a n d v e l o c i t y$ $b) h i s d i s t a n c e d o w n s t r e a m f r o m t h e s t a r t i n g p o i n t t i l l$ $w h e n h e r e a c h e s t h e o t h e r s i d e o f t h e r i v e r b a n k$ $c) t h e a c t u a l d i s t a n c e h e s w i m s t h r o u g h t h e w a t e r .$

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