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Show that x/(1+ x tan x,) x in (0,pi/2)i...

Show that `x/(1+ x tan x,) x in (0,pi/2)`is maximum when x = cos x.

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MODERN PUBLICATION-TEST PAPER 4-PROBLEM
  1. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

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  2. If A+B+C = pi, prove that [[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,c...

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  3. If A=[[1,2,3],[3,-2,1],[4,2,1]]"show that"A^3-23A-40I=0

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  4. Show that (a+1) is a factor of abs([(a+1),2,3],[1,a+1,3],[3,-6,a+1])

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  5. Find the dy/dx when x = a[cos t + log tan (t//2)], y = a sin t

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  6. Prove that: y = (4 sin theta)/(2 +cos theta)- theta is an increasing f...

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  7. inttan^-1(secx+tanx)dx

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  8. If the magnitude of the difference of two unit vectors is sqrt3 then f...

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  9. Find the equation of the plane if the point (5,-3,4) is the foot of th...

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  10. Proved that the line (x-1)/2=(y+2)/(-3)=(z-3)/1 lies on the plane 7x+5...

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  11. Find the points of intersection of the line (x-1)/1=(y+2)/ 3 =(z-1)/(...

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  12. Let A=Rxx R and be the binary operation on A defined by (a, b) *(c,d) ...

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  13. If A=[{:(1,2,0),(-2,-1,-2),(0,-1,1):}] then find A^-1 Using A^-1 solv...

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  14. If A=((cosx,sinx),(-sinx,cosx)) then prove that A^n=((cosnx,sin nx),(-...

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  15. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

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  16. If ysqrt(x^2 +1) = log{sqrt(x^2 +1)- x} then prove that (x^2 +1) dy/dx...

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  17. Show that x/(1+ x tan x,) x in (0,pi/2)is maximum when x = cos x.

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  18. Find the area enclosed by y^2=x^3,x=0,y=1

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  19. Solve y^(2)+x^(2)dy/dx=xydy/dx.

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  20. Prove the following by vector method. Altitudes of a triangle are conc...

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