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If y= (tan^(-1)x)^2, then show that (1+x...

If `y= (tan^(-1)x)^2,` then show that `(1+x^2)^2(d^2y)/(dx^2)+2x(1+x^2)(dy)/(dx) =2`.

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UNITED BOOK HOUSE-HIGHER SECONDARY EXAMINATION 2020.-EXERCISE
  1. Show that sin^(-1) (12/13)+cos^(-1)(4/5)+tan^(-1)(63/16) = pi.

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  2. If A = [[0,6,7],[-6,0,8],[7,-8,0]],B=[[0,1,1],[1,0,2],[1,2,0]],C=[[2],...

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  3. If A = ([cos theta,sin theta],[-sin theta,cos theta]) show that A= ([c...

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  4. show that |[1,x,x^2],[x^2,1,x],[x,x^2,1]| = (1-x^3)^2

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  5. If (cos x)^y = (cos y)^x then show that (dy)/(dx) = (y tan x+log cos y...

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  6. If y= (tan^(-1)x)^2, then show that (1+x^2)^2(d^2y)/(dx^2)+2x(1+x^2)(d...

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

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  8. Evaluate: int (sqrt(tanx)+sqrtcotx)dx

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  9. Solve: xy (dy)/(dx)=(x+2)(y+2), given x= 1, when y =-1.

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  10. Solve: x^2dy+(xy+y^2)dx=0, given x=1 and y = 1.

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  11. If vec a,vec b, vec c be three vectors such that vec a+vec b+vec c=0 ,...

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  12. Show that the points A=(2,-1,1),B=(1,-3,-5) and C=(3,-4,-4) are verti...

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  13. Show that: overset(1)underset(0)int (log(1+x)/(1+x^2))dx= pi/8 log 2.

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  14. Let A and B be two events such that P(A) =1/3,P(B)=1/4 and P(AnnB)=1/4...

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  15. Prove that all points of the curve y^2=4a[x+asinx/a] at which the lang...

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  16. Solve: (dy)/(dx)-3ycot x=sin2x, given y=2 when x= pi/2

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  17. Find two positive numbers x and y such that x + y = 60 and xy^(3) is m...

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  18. Evaluate the following integral overset(3)underset(1)int (x^2+x)dx.

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  19. A variable plane which is at a constant distance 3p from origin cuts t...

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  20. Find the equation of the plane which passes through the points (3,4,1)...

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