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Prove that : tan^-1 x +tan^-1 2x/(1-x^2)...

Prove that : `tan^-1 x +tan^-1 2x/(1-x^2) = tan^-1 ((3x-x^3)/(1-3x^2)), |x| < 1/sqrt3`

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MODERN PUBLICATION-MOCK TEST-2-EXERCISE
  1. Solve the differential equation : (x^2 + xy)dy=(x^2+y^2)dx.

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  2. Find the volume of the parallelopiped whose sides are given by vectors...

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  3. Prove that : tan^-1 x +tan^-1 2x/(1-x^2) = tan^-1 ((3x-x^3)/(1-3x^2)),...

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  4. Solve the following equations: tan^-1((1-x)/(1+x)) = 1/2 tan^-1 x, x...

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  5. If A=[[1,2,2],[2,1,2],[2,2,1]], verify that : A^2-4A-5I=O

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  6. Solve the following system of equations by matrix method, where xne0, ...

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  7. If xneynez and |[x,x^3,x^4-1],[y,y^3,y^4-1],[z,z^3,z^4-1]|=0, then pro...

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  8. If x^(y)=e^(x-y), then prove that (dy)/(dx)=(logx)/((1+logx)^(2))

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  9. If y=xlog[(ax)^-1+a^-1], prove that : x (x+1) (d^2y) / (dx^2) + xdy/dx...

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  10. Evaluate : int x^2/((x^2+1)(3x^2+4))dx

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  11. Evaluate : int1^4 (3x^2+2x)dx as the limit of sum.

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  12. Prove that : ""∫0 ^(pi/2)sin2xlogtanxdx=0

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  13. Find the particular solution of the differential equation (1+e^(2x))dy...

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  14. Using vectors, find the area of the triangle having vertices A (1, 1, ...

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  15. Find the co-ordinates of the foot of the perpendicualr drawn from the ...

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  16. There are 40 scholars in a class, out of which 10 are sports- persons....

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  17. let A = N xxN and * be the binary operation on A defined by : (a,b) * ...

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  18. Consider rrarr[4,infty] given by f(x)=x^2+4. Show that f is invertible...

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  19. Find the points of local maximum and local minimum, if any, of the fun...

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  20. Using integration find the area of region bounded by the triangle wher...

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