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DifferentiationQuestion and Answers: Page 3 |
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) |
Ω= ∫_1 ^( 3) (( 1)/( (√((x−1 )^3 )) + (√((x+1 )^3 )))) dx= ? |
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. |
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) ) |
What minimum value f(x,y)=x^2 +y^2 −z^2 when x+2y+4z=21 |
If f(x) =(x^2 −4x) sin 4x find f^((6)) (x). |
f(x)= ((3x−5)/(2x+1)) →f^′ (x)=....? |
y′′ + (2/x).y′ + y = 0 y=¿ |
f(tan x)+ 2f(cot x) = 4x f ′(x)= ? |
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 ) |
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 |
inf ∅ =^? +∞ and sup ∅ =^? −∞ |
Calcul ∫^( +∞) _( 0) ((lnt)/( (√t)(1+t^2 )))dt |
if y=sin x find (d^2 /dy^2 )cos^7 x |
Ω= ∫_0 ^( 1) (( (x−1)^( 2) )/(ln^2 (x))) dx= ? −−−− |
Ω = Σ_(m=1) ^∞ Σ_(n=1) ^∞ (((−1)^( n+1) )/(m^2 n + mn^( 2) )) = ? −−−−− |
(dy/dx) + (√((1−y^2 )/(1−x^2 ))) = 0 |
1. f(x)= { ((sinx , (π/2)<x≤2π)),((cosx , 0≤x≤(π/2))) :} then find the f^′ ((π/2)) =? 2. f(x)= { ((sinx , (π/2)<x≤2π)),((cosx , 0≤x≤(π/2))) :} then find the f′(2π) =? |