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if y = (x+sqrt(x^2+a^2))^n then prove th...

if `y = (x+sqrt(x^2+a^2))^n` then prove that `(dy)/(dx)= (ny)/(sqrt(x^2+a^2)`

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If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (a) (n y)/(sqrt(x^2+a^2)) (b) -(n y)/(sqrt(x^2+a^2)) (c) (n x)/(sqrt(x^2+a^2)) (d) -(n x)/(sqrt(x^2+a^2))

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If y="("x+sqrt(x^(2)-1)")"^(m) , then prove that, (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)+m^(2)y=0

UNITED BOOK HOUSE-SET 6-EXERCISE
  1. Find the value of |[1,1,1],[4,3,2],[4^2,3^2,2^2]|

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  2. f(x) = { (kx+1, x le pi),( cos x, x >pi):} If f(x) is continous at x =...

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  3. if y = (x+sqrt(x^2+a^2))^n then prove that (dy)/(dx)= (ny)/(sqrt(x^2+a...

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  4. Evaluate: int((cosx+xsinx)/(x(x+cosx)))dx.

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  5. Verify Rolle's theorem for the function f(x) = x^2+2x-8 in [-4,2]

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  6. Solve: (1+x^2)(dy)/(dx) = y+tan^(-1)x

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  7. If vec p is a unit vector and (vec x- vecp).(vec x+ vecp) = 8 then fin...

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  8. Find the intercepts made by the plane x-2y+3z-18=0 on the axes.

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  9. If P(A) = 5/13,P(B)= 6/13 and P(AuuB) = 7//13 then find P(bar A//B) a...

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  10. The mean and variance of a binomial distribution are 16 and 12 respect...

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  11. Prove that tan^(-1) {(sqrt(1+cos x)+sqrt(1-cosx))/(sqrt(1+cos x)-sqrt(...

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  12. Let A = [[1,0],[-1,7]] and I = [[1,0],[0,1]] then find the K when A^2=...

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  13. Show that A = [[1,2,2],[2,1,2],[2,2,1]] satrisfies the matrix equation...

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  14. If alpha,beta,gamma are in A.P. then show that , |[x-3,x-4,x-alpha],[x...

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  15. If sqrt(1-x^6)+sqrt(1-y^6) = a(x^3-y^3) then prove that (dy)/(dx)= x^2...

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  16. If y = (x+ sqrt(1+x^2))^n then prove that (1+x^2)y2+xy1 = n^2y.

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  17. Evaluate: int (dx)/(1+tanx)

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  18. Evaluate: int e^x (2-sin 2x)/(1-cos 2x)dx

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  19. Solve: (x+3)(dy)/(dx)-3y =(x+3)^5

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  20. Solve: y^2dx+(xy+x^2)dy =0

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