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DifferentiationQuestion and Answers: Page 3

Question Number 203063 Answers: 1 Comments: 0

Question Number 202866 Answers: 1 Comments: 0

calculate ... 𝛗= ∫_0 ^( 1) (( tanh^( −1) (x))/((1 + x )^( 2) )) dx = ?

$c a l c u l a t e . . .$ $ϕ = \int_{0}^{1} \frac{{t a n h}^{- 1} (x)}{{(1 + x)}^{2}} d x = ?$

Question Number 201940 Answers: 1 Comments: 0

tan^3 (xy^2 +y)=x find (dy/dx)

${t a n}^{3} ({x y}^{2} + y) = x f i n d \frac{d y}{d x}$

Question Number 201534 Answers: 0 Comments: 1

let f(x)=tanx find f^((n)) (x) with n integr natural

$l e t f (x) = t a n x$ $f i n d f^{(n)} (x) w i t h n i n t e g r$ $n a t u r a l$

Question Number 201214 Answers: 1 Comments: 0

A ball lies on the function z=xy at the point (1,2,2). Find the point in the xy−plane where the ball will touch it. (an unsolved old question Q200929)

$A ball lies on the function z = x y at$ $the point (1, 2, 2) . Find the point in$ $the x y - plane where the ball will$ $touch it .$ $(a n u n s o l v e d o l d q u e s t i o n Q 200929)$

Question Number 201140 Answers: 1 Comments: 0

If R_− =x^2 yi_− −2y^2 zj_− +xy^2 z^2 k_− , find ∣(d^2 R/dx^2 )×(d^2 R/dy^2 )∣ at the point (2,1,−2)

$I f \underline{R} = x^{2} y \underline{i} - 2 y^{2} z \underline{j} + {x y}^{2} z^{2} \underline{k}, f i n d ∣ \frac{d^{2} R}{{d x}^{2}} \times \frac{d^{2} R}{{d y}^{2}} ∣$ $a t t h e p o i n t (2, 1, - 2)$

Question Number 201133 Answers: 0 Comments: 1

Ω= ∫_1 ^( 3) (( 1)/( (√((x−1 )^3 )) + (√((x+1 )^3 )))) dx= ?

$Ω = \int_{1}^{3} \frac{1}{\sqrt{{(x - 1)}^{3}} + \sqrt{{(x + 1)}^{3}}} d x = ?$

Question Number 200738 Answers: 0 Comments: 0

Solve: A smooth sphere A,of mass 2kg and moving with speed 6ms^(−1) collides obliquely with a smooth sphere B of mass 4kg. just before the impact B is stationary and the velocity of A makes an angle of 10° with the lines of centers of the two sphere. The coefficient of restitution between the spheres is (1/2). Find the magnitude and directions of the velovities of A and B immediately after the impact.

$S o l v e : A s m o o t h s p h e r e A, o f m a s s 2 k g a n d$ $m o v i n g w i t h s p e e d 6 {m s}^{- 1} c o l l i d e s o b l i q u e l y$ $w i t h a s m o o t h s p h e r e B o f m a s s 4 k g . j u s t b e f o r e t h e i m p a c t B i s$ $s t a t i o n a r y a n d t h e v e l o c i t y o f A m a k e s$ $a n a n g l e o f 10 ° w i t h t h e l i n e s o f c e n t e r s o f t h e t w o s p h e r e .$ $T h e c o e f f i c i e n t o f r e s t i t u t i o n b e t w e e n t h e$ $s p h e r e s i s \frac{1}{2} . F i n d t h e m a g n i t u d e a n d$ $d i r e c t i o n s o f t h e v e l o v i t i e s o f A a n d B$ $i m m e d i a t e l y a f t e r t h e i m p a c t .$

Question Number 200418 Answers: 1 Comments: 0

calculus ( I ) If , I = ∫_0 ^( π) (( x )/(1 + sin^2 (x))) dx = a ζ ( 2 ) ⇒ a = ? where , ζ (s ) = Σ_(n=1) ^∞ (( 1)/n^( s) )

$calculus (I)$ $I f, I = \int_{0}^{π} \frac{x}{1 + \sin^{2} (x)} d x = a ζ (2)$ $\Rightarrow a = ?$ $w h e r e, ζ (s) = \underset{n = 1}{\sum^{\infty}} \frac{1}{n^{s}}$

Question Number 200251 Answers: 1 Comments: 0

Question Number 199459 Answers: 2 Comments: 0

What minimum value f(x,y)=x^2 +y^2 −z^2 when x+2y+4z=21

$What minimum value$ $f (x, y) = x^{2} + y^{2} - z^{2} when$ $x + 2 y + 4 z = 21$

Question Number 199261 Answers: 0 Comments: 0

Question Number 199176 Answers: 1 Comments: 0

If f(x) =(x^2 −4x) sin 4x find f^((6)) (x).

$If f (x) = (x^{2} - 4 x) \sin 4 x$ $find f^{(6)} (x) .$

Question Number 198988 Answers: 1 Comments: 0

Question Number 198953 Answers: 1 Comments: 0

f(x)= ((3x−5)/(2x+1)) →f^′ (x)=....?

$f (x) = \frac{3 x - 5}{2 x + 1} \to f^{^{'}} (x) = . . . . ?$

Question Number 198688 Answers: 1 Comments: 0

y′′ + (2/x).y′ + y = 0 y=¿

$y^{″} + \frac{2}{x} . y^{'} + y = 0$ $y = ¿$

Question Number 198562 Answers: 1 Comments: 0

f(tan x)+ 2f(cot x) = 4x f ′(x)= ?

$f (\tan x) + 2 f (\cot x) = 4 x$ $f^{'} (x) = ?$

Question Number 197664 Answers: 0 Comments: 1

Question Number 197317 Answers: 0 Comments: 0

if x = ((cos θ)/u) , y = ((sin θ)/u) and z = f(x,y) then show that (∂^2 z/∂x^2 ) + (∂^2 z/∂y^2 ) = u^4 (∂^2 z/∂u^2 ) + u^3 (∂z/∂u) + u^4 (∂^2 z/∂θ^2 )

$if x = \frac{\cos θ}{u}, y = \frac{\sin θ}{u} a n d z = f (x, y)$ $then show that$ $\frac{\partial^{2} z}{\partial x^{2}} + \frac{\partial^{2} z}{\partial y^{2}} = u^{4} \frac{\partial^{2} z}{\partial u^{2}} + u^{3} \frac{\partial z}{\partial u} + u^{4} \frac{\partial^{2} z}{\partial θ^{2}}$

Question Number 197277 Answers: 1 Comments: 0

Question Number 197057 Answers: 3 Comments: 2

Question Number 196902 Answers: 1 Comments: 0

Question Number 196691 Answers: 0 Comments: 2

Can someone recommend Calculus book , But I prefer if the book isn't boring and have a real challenging problems not a direct consequence of what is illustrated

Question Number 196628 Answers: 0 Comments: 0

inf ∅ =^? +∞ and sup ∅ =^? −∞

$i n f \emptyset \overset{?}{=} + \infty a n d s u p \emptyset \overset{?}{=} - \infty$

Question Number 196408 Answers: 2 Comments: 0

Calcul ∫^( +∞) _( 0) ((lnt)/( (√t)(1+t^2 )))dt

$Calcul {\int_{0}}^{+ \infty} \frac{lnt}{\sqrt{t} (1 + t^{2})} dt$

Question Number 196401 Answers: 3 Comments: 0

if y=sin x find (d^2 /dy^2 )cos^7 x

$if y = \sin x$ $find \frac{d^{2}}{d y^{2}} co s^{7} x$

Pg 1 Pg 2 Pg 3 Pg 4 Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10

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