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AllQuestion and Answers: Page 513

Question Number 162473 Answers: 1 Comments: 0

Question Number 162471 Answers: 2 Comments: 0

[reposted] find ∫_( 0) ^( (𝛑/2)) sin^8 (x)dx + ∫_( 0) ^( 1) sin^(-1) ((x)^(1/8) ) dx=?

$[r e p o s t e d]$ $f i n d \underset{0}{\int^{\frac{π}{2}}} \sin^{8} (x) d x + \underset{0}{\int^{1}} \sin^{- 1} (\sqrt[8]{x}) d x = ?$

Question Number 162429 Answers: 0 Comments: 1

put the digits 0,1,2,3,4,5,6,7,8,9,in place of the letters in order to perform the edditon

$p u t t h e d i g i t s 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, i n p l a c e o f t h e l e t t e r s i n o r d e r t o p e r f o r m t h e e d d i t o n$

Question Number 162424 Answers: 1 Comments: 0

calculate Ω = Σ_(n=1) ^∞ (( (−1)^( n) n)/(3^( n) (2n −1 ))) =? − Inspired from Sir Ghaderi′s post−

$c a l c u l a t e$ $Ω = \underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n} n}{3^{n} (2 n - 1)} = ?$ $- I n s p i r e d f r o m S i r G {h a d e r i}^{'} s p o s t -$

Question Number 162533 Answers: 5 Comments: 0

Question Number 162416 Answers: 1 Comments: 1

Prove that: ∫_( 0) ^( (𝛑/4)) ((4 ln (cotx))/(cos(2x + 2022𝛑))) dx = 3𝛇(2)

$Prove that :$ $\underset{0}{\int^{\frac{π}{4}}} \frac{4 \ln (\cot x)}{\cos (2 x + 2022 π)} dx = 3 ζ (2)$

Question Number 162417 Answers: 0 Comments: 4

Prove ∫_( 0) ^( (𝛑/2)) sin^8 (x) + ∫_( 0) ^( 1) sin^(-1) ((x)^(1/8) ) ≥ (π/2)

$Prove$ $\underset{0}{\int^{\frac{π}{2}}} \sin^{8} (x) + \underset{0}{\int^{1}} \sin^{- 1} (\sqrt[8]{x}) ⩾ \frac{π}{2}$

Question Number 162414 Answers: 1 Comments: 0

Prove the Identity for any (a,n) in Real Number (1 + a)∙a^([n]) = a ∙ a^(2[(n/2)]) + a^(2[((n+1)/2)]) [∗] Greatest Integer Function

$Prove the Identity for any (a, n) in Real Number$ $(1 + a) \cdot a^{[n]} = a \cdot a^{2 [\frac{n}{2}]} + a^{2 [\frac{n + 1}{2}]}$ $[*] Greatest Integer Function$

Question Number 162411 Answers: 0 Comments: 0

Prove the identity for any ′n′ in Real number [(n/2)] ∙ [((n + 1)/2)] = (1/4)([n]^2 + 2[(n/2)] - [n]) [∗] Greatest Integer Function

$Prove the identity for any^{'} n^{'} in Real number$ $[\frac{n}{2}] \cdot [\frac{n + 1}{2}] = \frac{1}{4} ({[n]}^{2} + 2 [\frac{n}{2}] - [n])$ $[*] Greatest Integer Function$

Question Number 162410 Answers: 1 Comments: 0

∫(dx/((a−cosx)^2 )) a>1

$\int \frac{d x}{{(a - c o s x)}^{2}} a > 1$

Question Number 162510 Answers: 1 Comments: 0

lim_(x→0) ((7tan x−tan 7x)/(3x)) =?

$\lim_{x \to 0} \frac{7 \tan x - \tan 7 x}{3 x} = ?$

Question Number 162509 Answers: 0 Comments: 0

find Σ_(n=1) ^∞ (((−1)^n )/(n^3 (2n+1)^4 ))

$find \sum_{n = 1}^{\infty} \frac{{(- 1)}^{n}}{n^{3} {(2 n + 1)}^{4}}$

Question Number 162399 Answers: 1 Comments: 1

Let m & n be two positive numbers greater than 1 . If lim_(p→0) ((e^(cos (p^n )) −e)/p^m ) = (1/2)e then (n/m)=?

$L e t m & n b e t w o p o s i t i v e n u m b e r s$ $g r e a t e r t h a n 1 . I f \lim_{p \to 0} \frac{e^{\cos (p^{n})} - e}{p^{m}} = \frac{1}{2} e$ $t h e n \frac{n}{m} = ?$

Question Number 162398 Answers: 1 Comments: 0

lim_(x→0) ((∫_0 ^1 (arctan (t+sin x)−arctan t)dt)/(arctan x))=?

$\lim_{x \to 0} \frac{\int_{0}^{1} (\arctan (t + \sin x) - \arctan t) dt}{\arctan x} = ?$

Question Number 162396 Answers: 1 Comments: 1

Question Number 162395 Answers: 0 Comments: 1

Question Number 162390 Answers: 0 Comments: 0

Question Number 162382 Answers: 2 Comments: 0

Question Number 162377 Answers: 1 Comments: 2

prove that ψ′′ ((1/4) )= −2π^( 3) − 56 ζ (3 )

$p r o v e t h a t$ $ψ^{″} (\frac{1}{4}) = - 2 π^{3} - 56 ζ (3)$

Question Number 162374 Answers: 0 Comments: 2

Question Number 162371 Answers: 2 Comments: 0

If x ∈R the maximum value of ((3x^2 +9x+17)/(3x^2 +9x+7)) is ...

$I f x \in R t h e m a x i m u m v a l u e$ $o f \frac{3 x^{2} + 9 x + 17}{3 x^{2} + 9 x + 7} i s . . .$

Question Number 162368 Answers: 1 Comments: 2

Question Number 162367 Answers: 1 Comments: 0

Let x_1 ,x_2 ,x_3 be the roots of the equation x^3 +3x+5=0 . Then the value of expression (x_1 +(1/x_1 ))(x_2 +(1/x_2 ))(x_3 +(1/x_3 )) is equal to

$L e t x_{1}, x_{2}, x_{3} b e t h e r o o t s o f t h e$ $e q u a t i o n x^{3} + 3 x + 5 = 0 . T h e n t h e$ $v a l u e o f e x p r e s s i o n (x_{1} + \frac{1}{x_{1}}) (x_{2} + \frac{1}{x_{2}}) (x_{3} + \frac{1}{x_{3}}) i s$ $e q u a l t o$

Question Number 162366 Answers: 1 Comments: 0

Given that the solution set of the quadratic inequality ax^2 +bx+c >0 is (2,3). Then the solution set of the inequality cx^2 +bx+a <0 will be

$G i v e n t h a t t h e s o l u t i o n s e t o f t h e$ $q u a d r a t i c i n e q u a l i t y {a x}^{2} + b x + c > 0$ $i s (2, 3) . T h e n t h e s o l u t i o n s e t$ $o f t h e i n e q u a l i t y {c x}^{2} + b x + a < 0$ $w i l l b e$

Question Number 162365 Answers: 0 Comments: 0

∫_0 ^1 ∫_0 ^1 ∫_0 ^1 ln^2 (x+y+z)dxdydz=?

$\underset{0}{\int^{1}} \underset{0}{\int^{1}} \underset{0}{\int^{1}} {l n}^{2} (x + y + z) d x d y d z = ?$

Question Number 162364 Answers: 2 Comments: 1

lim_(x→0) ((5sin x−sin 3x cos 2x−cos 3x sin 2x)/x^3 ) =?

$\lim_{x \to 0} \frac{5 \sin x - \sin 3 x \cos 2 x - \cos 3 x \sin 2 x}{x^{3}} = ?$

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