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Question Number 167002 Answers: 0 Comments: 0

calculate :: lim_(t→∞) 8∫_0 ^(π/2) e^x ∙sin (tx)∙sin (2tx)∙cos (3tx)∙cos (4tx)dx=?

$calculate :: \underset{t \to \infty}{\lim 8} \int_{0}^{π / 2} e^{x} \cdot \sin (tx) \cdot \sin (2 tx) \cdot \cos (3 tx) \cdot \cos (4 tx) dx = ?$

Question Number 167004 Answers: 0 Comments: 0

calculate :: lim_(x→(√π)) ∫_(√π) ^x (((x^2 +(√π)t)e^t^2 )/((x−(√π))(x^2 +π)t^2 lnt))dt=?

$calculate :: \lim_{x \to \sqrt{π}} \int_{\sqrt{π}}^{x} \frac{(x^{2} + \sqrt{π} t) e^{t^{2}}}{(x - \sqrt{π}) (x^{2} + π) t^{2} lnt} dt = ?$

Question Number 167003 Answers: 1 Comments: 0

Σ_(n=2) ^(n=∞) ((3/4))^n cos (180°n)= ?

$\underset{n = 2}{\sum^{n = \infty}} {(\frac{3}{4})}^{n} \cos (180 ° n) = ?$

Question Number 166994 Answers: 2 Comments: 0

1+1≠??

$1 + 1 \neq ? ?$

Question Number 166982 Answers: 1 Comments: 3

hi! help me! lim_(x→∞) ∫_0 ^∞ e^2 c(√x)∫_0 ^∞ =?

$hi!$ $help me!$ $\lim_{x \to \infty} \int_{0}^{\infty} e^{2} c \sqrt{x} \int_{0}^{\infty} = ?$

Question Number 167098 Answers: 3 Comments: 0

find the maximum of f(x)=sin x+cos x+sin x cos x

$f i n d t h e m a x i m u m o f$ $f (x) = \sin x + \cos x + \sin x \cos x$

Question Number 166975 Answers: 3 Comments: 3

hi ! help me ! lim_(x→−∞) (e^(1/(x+(√(x^2 +1)))) /x) = ???

$hi!$ $help me!$ $\underset{x \to - \infty}{l i m} \frac{e^{\frac{1}{x + \sqrt{x^{2} + 1}}}}{x} = ? ? ?$

Question Number 166959 Answers: 1 Comments: 0

γ=∫ ((e^x (sin x+1))/(cos x+1)) dx =?

$γ = \int \frac{e^{x} (\sin x + 1)}{\cos x + 1} dx = ?$

Question Number 166958 Answers: 3 Comments: 1

If polynomial x^3 −9x^2 +11x−1=0 have the roots are a,b an c . Given Δ = (√a) + (√b) + (√c) then Δ^4 −18Δ^2 −8Δ =?

$If polynomial x^{3} - {9 x}^{2} + 11 x - 1 = 0$ $have the roots are a, b an c .$ $Given Δ = \sqrt{a} + \sqrt{b} + \sqrt{c} then$ $Δ^{4} - 18 Δ^{2} - 8 Δ = ?$

Question Number 166956 Answers: 1 Comments: 0

calculate ∫_0 ^( ∞) (((√x) arctan(x))/(1+x^( 2) ))dx =?

$c a l c u l a t e$ $\int_{0}^{\infty} \frac{\sqrt{x} a r c t a n (x)}{1 + x^{2}} d x = ?$

Question Number 166954 Answers: 1 Comments: 0

Given x^3 −3x^2 (√2) +6x−2(√2)−8=0 then x^5 −41x^2 +2022 =?

$Given x^{3} - {3 x}^{2} \sqrt{2} + 6 x - 2 \sqrt{2} - 8 = 0$ $then x^{5} - {41 x}^{2} + 2022 = ?$

Question Number 166950 Answers: 0 Comments: 3

Question Number 166943 Answers: 1 Comments: 2

Question Number 166940 Answers: 1 Comments: 0

Question Number 166939 Answers: 1 Comments: 0

Question Number 166929 Answers: 1 Comments: 0

A particle of mass 0.25kg vibrates with a period of 2secs. If its greatest displacement is 0.4m. What is its maximum kinetic energy.

$A p a r t i c l e o f m a s s 0.25 k g v i b r a t e s$ $w i t h a p e r i o d o f 2 s e c s . I f i t s$ $g r e a t e s t d i s p l a c e m e n t i s 0.4 m . W h a t$ $i s i t s m a x i m u m k i n e t i c e n e r g y .$

Question Number 166928 Answers: 1 Comments: 0

Question Number 166926 Answers: 3 Comments: 0

lim_(n→∞) (5^n /(n!))=?

$\lim_{n \to \infty} \frac{5^{n}}{n!} = ?$

Question Number 166917 Answers: 2 Comments: 4

Question Number 166916 Answers: 0 Comments: 0

Ω= Σ_(n=1) ^∞ (( H_( n) )/(n(n+1))) = −−−−−− Ω = Σ_(n=1) ^∞ −(1/(n+1)) ∫_(0 ) ^( 1) x^( n−1) ln(1−x )dx = ∫_0 ^( 1) {−(1/x^2 )ln(1−x).Σ_(n=1) (x^( n+1) /(n+1))}dx = ∫_0 ^( 1) {((−ln(1−x))/x^( 2) )Σ_(n=2) ^∞ (x^( n) /n)}dx = ∫_0 ^( 1) ((−ln(1−x))/x^( 2) ) {−x +Σ_(n=1) ^∞ (x^( n) /n) }dx = −li_( 2) ( 1) +[ ∫_0 ^( 1) ((ln^( 2) ( 1−x ))/x^( 2) )dx=_(derived) ^(earlier) (π^( 2) /3) ] = −(π^( 2) /6) + (π^( 2) /3) = (( π^( 2) )/6) = ζ (2) ■ m.n

$Ω = \underset{n = 1}{\sum^{\infty}} \frac{H_{n}}{n (n + 1)} =$ $- - - - - -$ $Ω = \underset{n = 1}{\sum^{\infty}} - \frac{1}{n + 1} \int_{0}^{1} x^{n - 1} l n (1 - x) d x$ $= \int_{0}^{1} {- \frac{1}{x^{2}} l n (1 - x) . \sum_{n = 1} \frac{x^{n + 1}}{n + 1}} d x$ $= \int_{0}^{1} {\frac{- l n (1 - x)}{x^{2}} \underset{n = 2}{\sum^{\infty}} \frac{x^{n}}{n}} d x$ $= \int_{0}^{1} \frac{- l n (1 - x)}{x^{2}} {- x + \underset{n = 1}{\sum^{\infty}} \frac{x^{n}}{n}} d x$ $= - {l i}_{2} (1) + [\int_{0}^{1} \frac{{l n}^{2} (1 - x)}{x^{2}} d x \underset{d e r i v e d}{\overset{e a r l i e r}{=}} \frac{π^{2}}{3}]$ $= - \frac{π^{2}}{6} + \frac{π^{2}}{3} = \frac{π^{2}}{6} = ζ (2) ◼ m . n$

Question Number 166911 Answers: 1 Comments: 0

Question Number 166910 Answers: 1 Comments: 1

given that is prime,proof that (√p) is irrational

$g i v e n t h a t i s p r i m e, p r o o f t h a t \sqrt{p} i s$ $i r r a t i o n a l$

Question Number 166904 Answers: 1 Comments: 0

A pendulum has a period 2sec. The bob pulled aside a distance 8cm as the amplitude and release. Find the displacement of the bob 0.7sec after it has been released.

$A p e n d u l u m h a s a p e r i o d 2 s e c . T h e$ $b o b p u l l e d a s i d e a d i s t a n c e 8 c m a s$ $t h e a m p l i t u d e a n d r e l e a s e . F i n d t h e$ $d i s p l a c e m e n t o f t h e b o b 0.7 s e c a f t e r$ $i t h a s b e e n r e l e a s e d .$

Question Number 166881 Answers: 0 Comments: 0

Question Number 166922 Answers: 0 Comments: 0

calculate : lim_(x→1) (((1+x)^(1/x) (1+(1/x))^x −4)/((x−1)^2 ))=ln16−3

$calculate : \lim_{x \to 1} \frac{{(1 + x)}^{\frac{1}{x}} {(1 + \frac{1}{x})}^{x} - 4}{{(x - 1)}^{2}} = \ln 16 - 3$

Question Number 166921 Answers: 0 Comments: 1

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