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Differentiate tan ^(-1)(sqrt(1+x^2 )-1)...

Differentiate `tan ^(-1)(sqrt(1+x^2 )-1)/x` w,r,t. `tan ^(-1)x`

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UNITED BOOK HOUSE-SET 15-EXERCISE
  1. If f(x) = x^2-5x + 10 and A = [[1,-2],[3,4]], find f(A).

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  2. Solve for x: [[15-2x,11,10],[11-3x,17,16],[7-x,14,13]]=0

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  3. Differentiate tan ^(-1)(sqrt(1+x^2 )-1)/x w,r,t. tan ^(-1)x

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  4. Find if Lagrange's Mean Value Theorem is applicable to the function f...

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  5. Evaluate: int cos(logx)dx.

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  6. Show that a right triangle of given hypotenuse has maximum area, when ...

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  7. Find the interval in which f(x) = sinx + cos x.[x in [0, 2 pi]] increa...

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  8. Evaluate: underset(0)overset(1)int(1/(1+x))dx.

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  9. If vec a, vec b and vec c are such that veca xx vecb = vecc and vecb x...

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  10. Find the angle between the lines vecr = (2hati - hatj +3hatk) + lambda...

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  11. If P(A) = 2P(B) = 2/5 and P(B/A) = 1/3, find P(A/B) and P(AuuB).

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  12. A pair of dice is thrown 3 times. Find the probability of getting a do...

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  13. If tan^(-1) [(yz)/(xr)] + tan^(-1) [(zx)/(yr)]+ tan^(-1) [(xy)/(zr)] =...

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  14. If A = [[1,-1],[2,-1]],B = [[a,1],[b,-1]] and (A+B)^2 = A^2+B^2 find a...

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  15. Prove that, [[1+x,1,1],[1,1+y,1],[1,1,1+z]] = xyz(1 + 1/x+1/y+1/z)

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  16. Solve :[[x-2,2x-3,3x-4],[x-4,2x-9,3x-16],[x-8,2x-27,3x-64]]=0

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  17. If siny = x sin(a+y) then show that (dy)/(dx)= (sina)/(1-2xcos a+x^2).

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  18. Evaluate:int e^(4x)sin 3x dx

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  19. Evaluate:int (tan theta d theta)/(1-sin theta)

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  20. Solve:(x+y+1)dx + (2x+2y-1)dy = 0

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