Question and Answers Forum

All Questions Topic List

DifferentiationQuestion and Answers: Page 16

Question Number 152653 Answers: 1 Comments: 0

Ω :=∫_0 ^( ∞) (( e^( −x^( 3) ) . sin (x^( 3) ))/x)dx= ((ζ (2 ))/2) m.n...

$Ω := \int_{0}^{\infty} \frac{e^{- x^{3}} . s i n (x^{3})}{x} d x = \frac{ζ (2)}{2}$ $m . n . . .$

Question Number 152631 Answers: 1 Comments: 0

Question Number 152478 Answers: 2 Comments: 0

Question Number 152350 Answers: 1 Comments: 0

prove that .... 𝛗:=∫_0 ^( 1) (( x. ln^( 2) ( 1+ x ))/(1 + x^( 2) )) dx =(1/(96)) ln(2 ) ( π^( 2) + 4 ln^( 2) (2 ))....■ M.N..

$prove that . . . .$ $ϕ := \int_{0}^{1} \frac{x . {l n}^{2} (1 + x)}{1 + x^{2}} d x = \frac{1}{96} l n (2) (π^{2} + 4 {l n}^{2} (2)) . . . . ◼$ $M . N . .$

Question Number 152340 Answers: 1 Comments: 0

If x^2 +y^2 = 1 then find the maximum value of x^2 +4xy−y^2 .

$If x^{2} + y^{2} = 1 then find the maximum$ $value of x^{2} + 4 xy - y^{2} .$

Question Number 152310 Answers: 4 Comments: 0

Question Number 152244 Answers: 0 Comments: 0

𝛗 := ∫_0 ^( ∞) (( cos (x ).cosh (x ))/(cosh (πx )))dx=?

$ϕ := \int_{0}^{\infty} \frac{c o s (x) . c o s h (x)}{c o s h (π x)} d x = ?$

Question Number 152240 Answers: 1 Comments: 0

prove that.. csch (x)= (1/x) + Σ_(n=1) ^∞ ((2.(−1)^( n) x)/(n^( 2) π^( 2) + x^( 2) )) then find: Ω := ∫_0 ^( ∞) ((cosh (x )−(1/x))/x) dx=−ln(2)....■

$p r o v e t h a t . .$ $c s c h (x) = \frac{1}{x} + \underset{n = 1}{\sum^{\infty}} \frac{2 . {(- 1)}^{n} x}{n^{2} π^{2} + x^{2}}$ $t h e n f i n d :$ $Ω := \int_{0}^{\infty} \frac{c o s h (x) - \frac{1}{x}}{x} d x = - l n (2) . . . . ◼$

Question Number 152122 Answers: 1 Comments: 0

(√(3+(√(6+(√(9+...+(√(96+(√(99)))))))))) = ?

$\sqrt{3 + \sqrt{6 + \sqrt{9 + . . . + \sqrt{96 + \sqrt{99}}}}} = ?$

Question Number 151965 Answers: 2 Comments: 0

x , y ∈ R & sin(x )+ cos (y ) =1 then max ( sin(y) + cos (x) ) =? ....

$x, y \in R$ $& s i n (x) + c o s (y) = 1$ $t h e n m a x (s i n (y) + c o s (x)) = ?$ $. . . .$

Question Number 151954 Answers: 1 Comments: 0

nice...calculus 𝛗 := ∫_0 ^( (π/2)) x^( 3) . cot (x )dx =(a/(16)) a :=? m.n...

$n i c e . . . c a l c u l u s$ $ϕ := \int_{0}^{\frac{π}{2}} x^{3} . c o t (x) d x = \frac{a}{16}$ $a := ?$ $m . n . . .$

Question Number 151942 Answers: 0 Comments: 0

If x , y > 1 : Min ( (( x^( 4) )/((y −1 )^( 2) )) + (( y^( 4) )/(( x − 1 )^( 2) )) ) = ? ......■ ? m.n...

$If x, y > 1 :$ $Min (\frac{x^{4}}{{(y - 1)}^{2}} + \frac{y^{4}}{{(x - 1)}^{2}}) = ? . . . . . . ◼ ?$ $m . n . . .$

Question Number 151940 Answers: 1 Comments: 0

Question Number 151819 Answers: 1 Comments: 0

1. prove that : ∫_0 ^( ∞) (( e^( t) .ln(t ))/((1 + e^( t) )^( 2) )) dt=(1/2)(ln((π/2) )− γ )

$1 . p r o v e t h a t :$ $\int_{0}^{\infty} \frac{e^{t} . l n (t)}{{(1 + e^{t})}^{2}} d t = \frac{1}{2} (l n (\frac{π}{2}) - γ)$

Question Number 151803 Answers: 0 Comments: 0

Question Number 151744 Answers: 1 Comments: 0

show that.... F := ∫_0 ^( ∞) (( sin^( 4) (x^( 2) ) )/x^( 2) ) dx = (1/8) ( 4 − (√2) )(√π) .....■ ...m.n...

$s h o w t h a t . . . .$ $F := \int_{0}^{\infty} \frac{{s i n}^{4} (x^{2})}{x^{2}} d x = \frac{1}{8} (4 - \sqrt{2}) \sqrt{π} . . . . . ◼$ $. . . m . n . . .$

Question Number 151685 Answers: 1 Comments: 0

Find maximum value of function α(x)= (√(2x)) +(√(16−x)) +(√(35+x)) .

$F i n d m a x i m u m v a l u e o f f u n c t i o n$ $α (x) = \sqrt{2 x} + \sqrt{16 - x} + \sqrt{35 + x} .$

Question Number 151175 Answers: 0 Comments: 0

Question Number 151118 Answers: 1 Comments: 0

∫_0 ^( ∞) (( arctan((x/2))+arctan(2x))/(x^( 2) +1))=^? (π^( 2) /4)

$\int_{0}^{\infty} \frac{a r c t a n (\frac{x}{2}) + a r c t a n (2 x)}{x^{2} + 1} \overset{?}{=} \frac{π^{2}}{4}$

Question Number 151114 Answers: 1 Comments: 0

solve.... Q := ∫_0 ^( 1) ln (x ). ln ( 2− x )dx =? ...........■ m.n.1970...

$s o l v e . . . .$ $Q := \int_{0}^{1} l n (x) . l n (2 - x) d x = ? . . . . . . . . . . . ◼$ $m . n . 1970 . . .$

Question Number 150963 Answers: 1 Comments: 0

Given x ,y real number such that 0<(y/x)<(1/2). Find minimum value of ((2y)/(x−y)) +((3x)/(x+2y)) .

$G i v e n x, y r e a l n u m b e r s u c h t h a t$ $0 < \frac{y}{x} < \frac{1}{2} . F i n d m i n i m u m v a l u e$ $o f \frac{2 y}{x - y} + \frac{3 x}{x + 2 y} .$

Question Number 150828 Answers: 2 Comments: 0

∫_0 ^( ∞) (( sin^( 2) (x ))/(x(√x))) dx=^? (√π)

$\int_{0}^{\infty} \frac{{s i n}^{2} (x)}{x \sqrt{x}} d x \overset{?}{=} \sqrt{π}$

Question Number 150749 Answers: 0 Comments: 0

Prove That :: I := ∫_0 ^( ∞) ((( sin (x ).cos (x ))^( 4) )/(x . (√x) ))dx=(1/(32)) (2 (√2) −1 )(√( π)) ....■ ..m.n..

$Prove That ::$ $I := \int_{0}^{\infty} \frac{{(s i n (x) . c o s (x))}^{4}}{x . \sqrt{x}} d x = \frac{1}{32} (2 \sqrt{2} - 1) \sqrt{π} . . . . ◼$ $. . m . n . .$

Question Number 150747 Answers: 2 Comments: 0

prove :: Ω:=∫_0 ^( ∞) e^(−(√x)) .ln ((( x))^(1/4) )=^? 1−γ m.n..

$p r o v e ::$ $Ω := \int_{0}^{\infty} e^{- \sqrt{x}} . l n (\sqrt[4]{x}) \overset{?}{=} 1 - γ$ $m . n . .$

Question Number 150594 Answers: 1 Comments: 0

The function f(x)=e^x +x being differentiable and one to one , has a differentiable inverse f^(−1) (x). The value of (d/dx) (f^(−1) ) at point f(ln 2) is __

$The function f (x) = e^{x} + x being$ $differentiable and one to one,$ $has a differentiable inverse f^{- 1} (x) .$ $The value of \frac{d}{d x} (f^{- 1}) at point$ $f (\ln 2) is__$

Question Number 150590 Answers: 1 Comments: 0

Let g is the inverse function of f and f ′(x)=(x^(10) /(1+x^2 )). If g(2)= a then g ′(2) =__

$Let g is the inverse function of$ $f and f^{'} (x) = \frac{x^{10}}{1 + x^{2}} . If g (2) = a then$ $g^{'} (2) =__$

Pg 11 Pg 12 Pg 13 Pg 14 Pg 15 Pg 16 Pg 17 Pg 18 Pg 19 Pg 20

Terms of Service

Contact: info@tinkutara.com