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Prove that tan^(-1)sqrt(x) =(1)/(2) cos^...

Prove that `tan^(-1)sqrt(x) =(1)/(2) cos^(-1)((1-x)/(1+x)), x in (0, 1)`.

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SHARAM PUBLICATION-MODEL QUESTION PAPER-3-EXERCISE
  1. If A = {1, 2, 3}, B = {4, 5, 6, 7} and f = {(1, 4), (2, 5), (3, 6)} i...

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  2. if ** is the binary operation on N given by a**b= L. C. M of a and b. ...

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  3. Prove that tan^(-1)sqrt(x) =(1)/(2) cos^(-1)((1-x)/(1+x)), x in (0, 1)...

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  4. Sole the following LPP graphically Maximise Z=6x(1)+7x(2) Subject ...

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  5. If A=[{:(1,-2,2),(3,1,-1):}]andB=[{:(2,4),(1,2),(3,-1):}] , then veri...

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  6. Using elementary operation find the inverse of [(2,3),(5,7)]

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  7. Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=...

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  8. Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,...

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  9. Find the value of k if the function f(x) defined by f(x)={(2x-1,when x...

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  10. If y=log[x+sqrt(x^(2)+1)], then prove that (x^(2)+1)(d^(2)y)/(dx^(2))+...

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  11. If sin y = x sin (a + y) then show that (dy)/(dx)=(sin^2(a+y))/(sina)

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  12. Find the equations of the tangent to the curve x = sin 3t, y = cos 2t ...

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  13. If f(x) = a In x + bx^2 + x has extreme values at x= - 1 and x = 2 the...

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  14. Evaluate the following integrals : int(cos^(-1)x)/(sqrt(1-x^(2)))dx.

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  15. Evaluate int(sin x - cos x)dx.

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  16. Prove that int0^(pi/2)lnsinxdx=pi/2ln( 1 /2)

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  17. Determine the area the of the region between the curves y=cos x and y=...

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  18. Solve the differential equation (1+x^2)(dy)/(dx)+y= tan^(-1)x

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  19. Show by vector method that the line joining the points (1, 4, 2) and ...

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  20. Find the co-ordinates of the point where the perpendicular from the or...

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