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Question Number 57529 Answers: 0 Comments: 1

calculate Σ_(n=1) ^∞ (((−1)^n )/(n^3 (n+1)))

$c a l c u l a t e \sum_{n = 1}^{\infty} \frac{{(- 1)}^{n}}{n^{3} (n + 1)}$

Question Number 57525 Answers: 1 Comments: 0

Question Number 57522 Answers: 3 Comments: 3

The radius of circle having minimum area,which touches the curve y=4−x^2 and the lines y=∣x∣ is ?

$T h e r a d i u s o f c i r c l e h a v i n g m i n i m u m$ $a r e a, w h i c h t o u c h e s t h e c u r v e y = 4 - x^{2}$ $a n d t h e l i n e s y =∣ x ∣ i s ?$

Question Number 57521 Answers: 2 Comments: 1

Question Number 57515 Answers: 1 Comments: 4

Question Number 57513 Answers: 0 Comments: 4

There are 128 players in the first round of a knockout competition. Half of the players were knocked out in each round. How many players took part in the fourth round? How many rounds were there in this competion?

$There are 128 players in the first round$ $of a knockout competition . Half of the$ $players were knocked out in each round .$ $How many players took part in the$ $fourth round ? How many rounds were there$ $in this competion ?$

Question Number 57494 Answers: 1 Comments: 1

Question Number 57491 Answers: 1 Comments: 0

If R is a region enclosed by y = f(x), y = g(x), x = a, x = b, is it possible to have f(x) and g(x) such that the center of gravity (x^ , y^ ) is not inside R ?

$If R is a region enclosed by y = f (x), y = g (x), x = a, x = b,$ $is it possible to have f (x) and g (x) such that$ $the center of gravity (\bar{x}, \bar{y}) is not inside R ?$

Question Number 57490 Answers: 1 Comments: 2

1)findF(a)= ∫_0 ^∞ ((cos(ln(2+x^2 )))/(a^2 +x^2 ))dx witha>0 2) find the value of ∫_0 ^∞ ((cos(ln(2+x^2 )))/(4+x^2 ))dx.

$1) f i n d F (a) = \int_{0}^{\infty} \frac{c o s (l n (2 + x^{2}))}{a^{2} + x^{2}} d x w i t h a > 0$ $2) f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{c o s (l n (2 + x^{2}))}{4 + x^{2}} d x .$

Question Number 57489 Answers: 1 Comments: 1

find the value of Σ_(n=2) ^∞ ((3n^2 +1)/((n−1)^3 (n+1)^3 ))

$f i n d t h e v a l u e o f \sum_{n = 2}^{\infty} \frac{3 n^{2} + 1}{{(n - 1)}^{3} {(n + 1)}^{3}}$

Question Number 57488 Answers: 1 Comments: 1

let A_n =∫_0 ^n ((t[t])/(3+t^2 ))dt 1)calculate lim_(n→+∞) A_n 2) find nature if Σ A_n

$l e t A_{n} = \int_{0}^{n} \frac{t [t]}{3 + t^{2}} d t$ $1) c a l c u l a t e {l i m}_{n \to + \infty} A_{n}$ $2) f i n d n a t u r e i f Σ A_{n}$

Question Number 57487 Answers: 0 Comments: 1

calculate lim_(x→1) ∫_x ^x^2 ((arctan(t))/(sint))dt .

$c a l c u l a t e {l i m}_{x \to 1} \int_{x}^{x^{2}} \frac{a r c t a n (t)}{s i n t} d t .$

Question Number 57486 Answers: 0 Comments: 4

let f(x) =((ln(1+x))/(2−x^2 )) 1)calculate f^((n)) (x) 2) calculate f^((n)) (0) 3)developp f(x) at integr serie.

$l e t f (x) = \frac{l n (1 + x)}{2 - x^{2}}$ $1) c a l c u l a t e f^{(n)} (x)$ $2) c a l c u l a t e f^{(n)} (0)$ $3) d e v e l o p p f (x) a t i n t e g r s e r i e .$

Question Number 57480 Answers: 0 Comments: 2

if F(x,y)=F(y,x) and x+y=c (constant) prove that F_(max or min) =F((c/2),(c/2)).

$i f F (x, y) = F (y, x) a n d x + y = c (c o n s t a n t)$ $p r o v e t h a t F_{m a x o r m i n} = F (\frac{c}{2}, \frac{c}{2}) .$

Question Number 57474 Answers: 1 Comments: 2

prove sin18×cos36=(1/4)

$prove$ $s i n 18 \times c o s 36 = \frac{1}{4}$

Question Number 57469 Answers: 0 Comments: 3

((4tan75)/(1−tan^2 75))=(1/(cos150)) find tan75 in surd form

$\frac{4 t a n 75}{1 - {t a n}^{2} 75} = \frac{1}{c o s 150}$ $f i n d t a n 75 i n s u r d f o r m$

Question Number 57462 Answers: 0 Comments: 0

Two conductors has total charge of +10.0μC and −10μC with 10volt between them. (a) Determine the capacitance between them (b) what is the p.d between the two condoctors if the charge on each are increased to +100μC and −100μC respectively ?

$Two conductors has total charge of$ $+ 10.0 μ C and - 10 μ C with 10 volt$ $between them .$ $(a) Determine the capacitance between them$ $(b) what is the p . d between the two$ $condoctors if the charge on each$ $are increased to + 100 μ C and$ $- 100 μ C respectively ?$