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Question Number 34420 Answers: 1 Comments: 1

let A = arctanx −arctany give another form of A if xy≠−1 .

$l e t A = a r c t a n x - a r c t a n y$ $g i v e a n o t h e r f o r m o f A i f x y \neq - 1 .$

Question Number 34421 Answers: 0 Comments: 1

let A = ∫_(−∞) ^(+∞) (dx/(x^2 −j)) with j=e^(i((2π)/3)) extract ReA and Im(A) and calculste its values.

$l e t A = \int_{- \infty}^{+ \infty} \frac{d x}{x^{2} - j} w i t h j = e^{i \frac{2 π}{3}}$ $e x t r a c t R e A a n d I m (A) a n d c a l c u l s t e i t s v a l u e s .$

Question Number 34411 Answers: 0 Comments: 5

Question Number 34410 Answers: 0 Comments: 0

Prove that (((n^2 )!)/((n!)^(n+1) )) is always an integer for n∈N.

$P r o v e t h a t \frac{(n^{2})!}{{(n!)}^{n + 1}} i s a l w a y s a n i n t e g e r$ $f o r n \in N .$

Question Number 34408 Answers: 0 Comments: 1

what is the value of (√(5(√(5(√(5(√(5(√(5(√5))))))))))) ignoring 64.

$w h a t i s t h e v a l u e o f$ $\sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5 \sqrt{5}}}}}}$ $i g n o r i n g 64 .$

Question Number 34385 Answers: 0 Comments: 0

p,q∈P m,n∈{0,1,2,...} How many pairs are there,whose LCM is p^m q^(n ) ,when: (i)(a,b) & (b,a) are considered same. (ii)(a,b) & (b,a) are considered different. (Generalization of Q# 34358)

$p, q \in P$ $m, n \in {0, 1, 2, . . .}$ $How many pairs are there, whose$ $LCM is p^{m} q^{n}, when :$ $(i) (a, b) & (b, a) are considered same .$ $(ii) (a, b) & (b, a) are considered different .$ $You can't use 'macro parameter character #' in math mode$

Question Number 34382 Answers: 1 Comments: 0

how do i prove ∫_o ^t cos 2(ωt+α)dt=0

$how do i prove$ $\int_{o}^{t} \cos 2 (ω t + α) dt = 0$

Question Number 34376 Answers: 0 Comments: 0

How to do A4 size page layout in equation editor ?

$H o w t o d o A 4 s i z e p a g e l a y o u t i n e q u a t i o n e d i t o r ?$

Question Number 34375 Answers: 1 Comments: 0

The value of lim_(x→(π/2)) (([(x/2)])/(log (sin x))) = ? [.]= greatest integer function.

$T h e v a l u e o f$ ${l i m}_{x \to \frac{π}{2}} \frac{[\frac{x}{2}]}{\log (\sin x)} = ?$ $[.] = g r e a t e s t i n t e g e r f u n c t i o n .$

Question Number 34374 Answers: 2 Comments: 0

lim_(x→1) {1−x+[x−1]+[1−x]} = ? [.]= greatest integer function.

${l i m}_{x \to 1} {1 - x + [x - 1] + [1 - x]} = ?$ $[.] = g r e a t e s t i n t e g e r f u n c t i o n .$

Question Number 34369 Answers: 1 Comments: 0

Determine number of possible pairs,whose GCD is 144 in case: (i) when (a,b) and (b,a) is considerd same. (ii) when (a,b) and (b,a) is considerd different.

$Determine number of possible pairs, whose$ $GCD is 144 in case :$ $(i) when (a, b) and (b, a) is considerd$ $same .$ $(ii) when (a, b) and (b, a) is considerd$ $different .$

Question Number 34367 Answers: 1 Comments: 0

Evaluate lim_(n→∞) ((n/(n^2 +1^2 ))+(n/(n^2 +2^2 ))+.....+(n/(n^2 +n^2 ))).

$Evaluate$ $\lim_{n \to \infty} (\frac{n}{n^{2} + 1^{2}} + \frac{n}{n^{2} + 2^{2}} + . . . . . + \frac{n}{n^{2} + n^{2}}) .$

Question Number 34365 Answers: 1 Comments: 0

if a>b>0 prove that b<((ae^x +be^(−x) )/(e^x +e^(−x) ))<a

$if a > b > 0 prove that$ $b < \frac{{ae}^{x} + {be}^{- x}}{e^{x} + e^{- x}} < a$

Question Number 34361 Answers: 1 Comments: 0

A right prism has a regular hexagonal base with sides of length 15cm,and a height of 20cm. find its volume and total surface area.

$A right prism has a regular$ $hexagonal base with sides of$ $length 15 cm, and a height$ $of 20 cm . find its volume and$ $total surface area .$

Question Number 34358 Answers: 1 Comments: 1

Determine number of possible pairs whose LCM is 144 in case, (i)when (a,b) & (b,a) are considered same. (ii)when(a,b) & (b,a) are considered different.

$Determine number of possible pairs whose$ $LCM is 144 in case,$ $(i) when (a, b) & (b, a) are considered same .$ $(ii) when (a, b) & (b, a) are considered different .$

Question Number 34357 Answers: 1 Comments: 0

If a+b+c=0 prove that i)((a/(b+c))+ (b/(c+a)) +(c/(a+b)))(((b+c)/a) +((c+a)/b) +((a+b)/c))=9 ii)((a/(b−c)) +(b/(c−a)) +(c/(a−b)))(((b−c)/a) +((c−a)/b) +((a−b)/c))=9

$I f a + b + c = 0 p r o v e t h a t$ $i) (\frac{a}{b + c} + \frac{b}{c + a} + \frac{c}{a + b}) (\frac{b + c}{a} + \frac{c + a}{b} + \frac{a + b}{c}) = 9$ $i i) (\frac{a}{b - c} + \frac{b}{c - a} + \frac{c}{a - b}) (\frac{b - c}{a} + \frac{c - a}{b} + \frac{a - b}{c}) = 9$