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DifferentiationQuestion and Answers: Page 14

Question Number 158691 Answers: 1 Comments: 0

Σ_(n=1) ^∞ (( (−1)^( n) H_( 2n) )/(2n)) =?

$\underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n} H_{2 n}}{2 n} = ?$

Question Number 158503 Answers: 0 Comments: 5

Question Number 158489 Answers: 0 Comments: 0

find the partial derivatives of the function with respect to each variable f(x,y)=∫_x ^y g(t) dt

$f i n d t h e p a r t i a l d e r i v a t i v e s o f t h e f u n c t i o n$ $w i t h r e s p e c t t o e a c h v a r i a b l e$ $f (x, y) = \int_{x}^{y} g (t) d t$

Question Number 158322 Answers: 0 Comments: 0

prove that: Σ_(n=1) ^∞ tan^( −1) ( (1/F_( n) ) ).tan^( −1) ( (1/F_( n+1) ) )= (π^( 2) /8) Fibonacci numbers

$p r o v e t h a t :$ $\underset{n = 1}{\sum^{\infty}} {t a n}^{- 1} (\frac{1}{F_{n}}) . {t a n}^{- 1} (\frac{1}{F_{n + 1}}) = \frac{π^{2}}{8}$ $F i b o n a c c i n u m b e r s$

Question Number 158293 Answers: 3 Comments: 0

question# If , Ω =∫_0 ^( 1) ((ln^( 2) (1−x^( 4) ))/x) dx= a ζ b) find the value of , a , b .

$You can't use 'macro parameter character #' in math mode$ $If, Ω = \int_{0}^{1} \frac{{l n}^{2} (1 - x^{4})}{x} d x = a ζ b)$ $f i n d t h e v a l u e o f, a, b .$

Question Number 158259 Answers: 1 Comments: 1

Given x,y∈R^+ and ((x/5)+(y/3))((5/x)+(3/y))=139. If maximum and minimum of ((x+y)/( (√(xy)) )) is M and n respectively, then what the value of 3M−4n.

$G i v e n x, y \in R^{+} a n d (\frac{x}{5} + \frac{y}{3}) (\frac{5}{x} + \frac{3}{y}) = 139 .$ $I f m a x i m u m a n d m i n i m u m$ $o f \frac{x + y}{\sqrt{x y}} i s M a n d n r e s p e c t i v e l y,$ $t h e n w h a t t h e v a l u e o f 3 M - 4 n .$

Question Number 158625 Answers: 0 Comments: 1

EI(∂^4 y/∂x^4 )+ρS(∂^2 y/∂t^2 )=0 (1) y(x,0)=U_0 (x) (∂y/∂t)(x,0)=V_0 (x) ; EI(∂^2 y/∂x^2 )(0,t)=EI(∂^2 y/∂x^2 )(L,t)=0

$E I \frac{\partial^{4} y}{\partial x^{4}} + ρ S \frac{\partial^{2} y}{\partial t^{2}} = 0 (1)$ $y (x, 0) = U_{0} (x)$ $\frac{\partial y}{\partial t} (x, 0) = V_{0} (x); E I \frac{\partial^{2} y}{\partial x^{2}} (0, t) = E I \frac{\partial^{2} y}{\partial x^{2}} (L, t) = 0$

Question Number 158156 Answers: 1 Comments: 0

solve : ( x^( 2) +x −6)^( 3) + (7x^( 2) −9x −2)^( 3) −512(x^2 −x−1)^( 3) =0 x = ?

$s o l v e :$ ${(x^{2} + x - 6)}^{3} + {(7 x^{2} - 9 x - 2)}^{3} - 512 {(x^{2} - x - 1)}^{3} = 0$ $x = ?$

Question Number 158064 Answers: 1 Comments: 0

Make tangen line at point (2,3).

$Make tangen line at point$ $(2, 3) .$

Question Number 158060 Answers: 1 Comments: 0

Question Number 158049 Answers: 2 Comments: 0

Find derivative of this function 1). f(x)= x.sin x 2). f(x)= e^(5x) . log _2 (3x) 3). f(x)= 3^(3x) .(2x−1) 4). f(x)= ((3x^2 −2)/(4x+1))

$Find derivative of this function$ $1) . f (x) = x . \sin x$ $2) . f (x) = e^{5 x} . \log_{2} (3 x)$ $3) . f (x) = 3^{3 x} . (2 x - 1)$ $4) . f (x) = \frac{{3 x}^{2} - 2}{4 x + 1}$

Question Number 157952 Answers: 1 Comments: 0

f(x)=x^(2014) +2x^(2013) +3x^(2012) +4x^(2011) +...+2014x+2015 min f(x)=?

$f (x) = x^{2014} + 2 x^{2013} + 3 x^{2012} + 4 x^{2011} + . . . + 2014 x + 2015$ $m i n f (x) = ?$

Question Number 157947 Answers: 1 Comments: 0

What are the coordinates of the points on the curve x^2 −y^2 =16 which nearest to (0,6)?

$W h a t a r e t h e c o o r d i n a t e s o f t h e$ $p o i n t s o n t h e c u r v e x^{2} - y^{2} = 16$ $w h i c h n e a r e s t t o (0, 6) ?$

Question Number 157665 Answers: 2 Comments: 0

Question Number 157382 Answers: 1 Comments: 0

Question Number 157278 Answers: 3 Comments: 0

Question Number 157247 Answers: 3 Comments: 0

F(x,y)=x^2 −2xy+6y^2 −12x+2y+45 find x &y such that F(x,y) minimum

$F (x, y) = x^{2} - 2 x y + 6 y^{2} - 12 x + 2 y + 45$ $f i n d x & y s u c h t h a t F (x, y) m i n i m u m$

Question Number 157169 Answers: 1 Comments: 0

Question Number 157116 Answers: 1 Comments: 2

max ∧ min of f(x) =(√x) +4(√((1−x)/2))

$m a x \land m i n o f f (x) = \sqrt{x} + 4 \sqrt{\frac{1 - x}{2}}$

Question Number 156864 Answers: 0 Comments: 4

φ := ∫_0 ^( 1) (( ln (1−x^( 2) ))/(1+ x^( 2) )) dx = proof : φ = ∫_0 ^( 1) (( ln(1−x ))/(1+x^( 2) ))dx + (π/8)ln(2) .... I= ∫_0 ^( 1) ((ln ( 1−x ))/(1+x^( 2) ))dx =^(x=tan(t)) ∫_0 ^( (π/4)) ln( cos(t)−sin(t))dt−∫_0 ^( (π/4)) ln(cos(t))dt = ∫_0 ^( (π/4)) ln((√2) )dt +∫_0 ^( (π/4)) ln(sin((π/4) −t))dt−(G/2) +(π/4)ln(2) =((3π)/8) ln(2)−(G/2) −(G/2) −(π/4) ln(2)=(π/8)ln(2)−G φ = (π/4)ln(2) − G ■ m.n

$ϕ := \int_{0}^{1} \frac{l n (1 - x^{2})}{1 + x^{2}} d x =$ $p r o o f :$ $ϕ = \int_{0}^{1} \frac{l n (1 - x)}{1 + x^{2}} d x + \frac{π}{8} l n (2)$ $. . . . I = \int_{0}^{1} \frac{l n (1 - x)}{1 + x^{2}} d x$ $\overset{x = t a n (t)}{=} \int_{0}^{\frac{π}{4}} l n (c o s (t) - s i n (t)) d t - \int_{0}^{\frac{π}{4}} l n (c o s (t)) d t$ $= \int_{0}^{\frac{π}{4}} l n (\sqrt{2}) d t + \int_{0}^{\frac{π}{4}} l n (s i n (\frac{π}{4} - t)) d t - \frac{G}{2} + \frac{π}{4} l n (2)$ $= \frac{3 π}{8} l n (2) - \frac{G}{2} - \frac{G}{2} - \frac{π}{4} l n (2) = \frac{π}{8} l n (2) - G$ $ϕ = \frac{π}{4} l n (2) - G ◼ m . n$

Question Number 156824 Answers: 1 Comments: 0

If x − z = tan^(− 1) (yz) and z = z(x, y), find ((δz)/(δx)) , ((δz)/(δy))

$If x - z = \tan^{- 1} (yz) and z = z (x, y), find \frac{δ z}{δ x}, \frac{δ z}{δ y}$

Question Number 156617 Answers: 1 Comments: 0

Question Number 156584 Answers: 1 Comments: 1

find p if y=1−px−3x^2 if the maximum is 13 (help pls)

$find p if y = 1 - px - {3 x}^{2}$ $if the maximum is 13 (help pls)$

Question Number 156386 Answers: 1 Comments: 0

φ (n )= Σ_(k=1) ^n (−1 )^( k−1) ((( n)),(( k)) ) H_( k) Find the value of : Σ_(n=1) ^∞ (−1)^( n−1) φ ( n^( 2) ) =?

$ϕ (n) = \underset{k = 1}{\sum^{n}} {(- 1)}^{k - 1} (\begin{matrix} n \\ k \end{matrix}) H_{k}$ $Find the value of :$ $\underset{n = 1}{\sum^{\infty}} {(- 1)}^{n - 1} ϕ (n^{2}) = ?$

Question Number 156206 Answers: 1 Comments: 0

Ω :=∫_0 ^( 1) (√x) (√(1−(√x) )) (√(1−(√(1−(√x) )))) dx=?

$Ω := \int_{0}^{1} \sqrt{x} \sqrt{1 - \sqrt{x}} \sqrt{1 - \sqrt{1 - \sqrt{x}}} d x = ?$

Question Number 156137 Answers: 1 Comments: 0

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