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DifferentiationQuestion and Answers: Page 2
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Question and Answers Forum |
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DifferentiationQuestion and Answers: Page 2 |
| u_0 = a, u_(n+1) = (√(u_n v_n )) v_0 = b ∈ ]0,1[ , v_(n+1) = (1/(2(u_n +v_n ))) • show that a≤u_n ≤u_(n+1) ≤v_n ≤v_(n+1) ≤b • show that v_n − u_n ≤ ((a+b)/2^n ) |
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| If x^m .y^n = (x + y)^(m + n) then (d^2 y/dx^2 ) = ? |
| If e^y (x + 1) = 1 then prove that (d^2 y/dx^2 ) = ((dy/dx))^2 . |
| If y = (1 + x)(1 + x^2 )(1 + x^4 ) .... (1 + x^(2n) ) then find (dy/dx) at x = 0. |
| f(x)=tan^2 x (√(tan x((tan x((tan x((tan x(√(...))))^(1/5) ))^(1/4) ))^(1/3) )) f ′((π/4))=? |
| ∫_0 ^( 1) (( ln(1−x )ln(1+x ))/x)dx = Σ_(n=1) ^∞ Ω_n find : Σ_(n=1) ^∞ n Ω_n = ? |
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| x^3 +y^3 =1 find the implceat second derivative |
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| ∫_1 ^∞ (x/(x^3 +lnx)) dx=? |
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| if y=(x)^(1/7) prove that y^′ =(1/(7 (x^6 )^(1/7) )) |
| Ω= ∫_(1/e) ^( e) (( arctan(x))/x) dx=? |
| prove that: (e)^(1/4) < ∫_0 ^( 1) e^( t^2 ) dt< ((1 + e)/2) |
| A rectangular enclosure is to be made against a straight wall using three lengths of fencing. The total length of the fencing available is 50m. Show that the area of the enclosure is 50x − 2x^2 , where x is the length of the sides perpendicular to the wall. Hence find the maximum area of the enclosure. |
| If , f : [ 0 , b] →^(continuous) R , g : R →_(b−periodic) ^(continuous) R ⇒ lim_(n→∞) ∫_0 ^( b) f(x)g(nx)dx=^? (1/b) ∫_0 ^( b) f(x)dx .∫_0 ^( b) g(x)dx |
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