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Determine the values of x for which the ...

Determine the values of x for which the function `f(x)= x^x, xgt0` is increasing or decreasing.

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. If e^x+e^y=e^(x+y), find dy/dx.

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  2. If x^7y^3=(x+y)^10, then find (d^2y)/(dx^2)

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  3. Determine the values of x for which the function f(x)= x^x, xgt0 is in...

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  4. If x=cos^-1(1/(sqrt(1+t^2))), y=sin^-1(1/(sqrt(t^2+1))) then dy/dx is ...

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  5. Find the angle between the tangents to the curve y=x^2-5x+6 at the poi...

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  6. Find the area of the region bounded by y=6x-x^2x-axis and between ordi...

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  7. intsin^-1sqrt(x/(a+x))dx=.

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  8. Solve : xdy/dx+y=xy^2

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  9. Evaluate int3^6sqrtx/(sqrt((9-x))+sqrtx)dx

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  10. Evaluate int-1^2 {|x\|+[x]}dx

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  11. The plane 4x+7y+4z+81=0 is rotated through a right angle about its lin...

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  12. If G is the centroid of a triangle ABC, prove that vec(GA)+vec(GB)+vec...

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  13. Find the image of the point (2,-1,3) in the plane 3x-2y+z-9=0

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  14. Prove that the measure of the angle between two main diagonals of a cu...

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  15. Show that the vectors 4hati+4hatj+ 4hatk,7hati+6hatj-hatk and 3hati+2h...

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  16. Integrate intdx/(x^4+1)

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  17. Solve x^2ydx-(x^3+y^3)dy=0.

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  18. Prove by vector method that in any triangle ABC, a/sinA=b/sinB=c/sinC.

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  19. If a line in the space makes angles alpha, beta  and gamma  with the c...

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  20. If the mapping f and g are given by f= {(1,2), (3, 4), (5, 6), (7, 8)}...

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