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Evalute: overset(pi//2)underset(0)int si...

Evalute: `overset(pi//2)underset(0)int sin^(3//2)x/(sin^(3//2)x+cos^(3//2)x)dx`

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UNITED BOOK HOUSE-SET 9-EXERCISE
  1. answer any one question : (ii) prove that , tan(pi/4 +1/2 (cos ^(-1) (...

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  2. If A = [[3,1],[-1,2]],I= [[1,0],[0,1]] and O = [[0,0],[0,0]] show that...

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  3. Show that, A = 1/3[[1,2,2],[2,1,-1],[-2,2,-1]] are orthogonal matrix a...

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  4. Solve for x |x-2 , 2x-3, 3x-4,x-4 ,2x-9, 3x-16 ,x-8, 2x-27, 3x-64|=0.

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  5. Show that the following determinant is a perfect square |[1,a,a^2],[a^...

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

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  7. Let y = (sin^(-1)x)^2+(cos^(-1)x)^2 show that (1-x^2)(d^2y)/(dx^2)-x(d...

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  8. Evaluate: int (dx)/(1+x^3)

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  9. Evaluate: int (x^2dx)/(x^4-x^2+1).

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  10. Solve: xdx+ ydy+ (xdy-ydx)/(x^2+y^2)=0 given y = 1 when x= 1.

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  11. Solve: (x+tany)dy = sin 2y dx.

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  12. D,E,F are the midpoints of the sides bar(BC),bar(CA) and bar(AB) respe...

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  13. The dot product of a vector with the vectors hat i-3 hatk,hat i-2 hatk...

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  14. Evalute: overset(pi//2)underset(0)int sin^(3//2)x/(sin^(3//2)x+cos^(3/...

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  15. The probability distribution of a discrete random varible X is as fol...

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  16. A ballong leaves the ground 50 ft from an observer. If it rises vertic...

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  17. A particle moves in a straight line such that its distance x from a fi...

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  18. Find the area of the region {(x , y): y^2lt=4x ,4x^2+4y^2lt=9}

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  19. Find the shortest distance between the lines (x-1)/2=(y-2)/3=(z-3)/4...

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  20. Find the distance between the point P(6,5,9) and the plane passing thr...

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