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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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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. If y=sqrt(x+1)Find deltay and dy when X=8 and dx=0.02.

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  2. Shows that the following functions do not possess maximum or minimum. ...

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

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  4. If x =sin t,y = sin 2t then prove that (1-x^2)(d^2y)/(dx^2)- x dy/dx +...

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  5. Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = ...

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  6. Solve xsin""y/xdy=(ysin""y/x-x)dx

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  7. Evaluate int0^(pi/2)sinx/(sinx+cosx)dx.

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  8. Determine the area within the ellipse x^2/a^2+y^2/b^2=1.

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  9. Integrate the following int[(2x+1)/sqrt(x^2+10x+29)]dx

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  10. If veca=hati+2hatj-3hatkand vecb=3hati-hatj+2hatk,then find the angle ...

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  11. Find the equation of plane passing through the intersection of the pla...

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  12. Find the co-ordinates of the foot of the perpendicular from the point ...

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  13. Prove that (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxxhatk)^2=2veca^2

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  14. Prove that the line (x+5)/3=(y+4)/1=(z-7)/-2 and x/1=(y+7)/5=(z-16)/-1...

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  15. Evaluate the following integrals int(3)/(x^3-1)dx

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  16. Show that int0^pixInsinx=pi^2/2In1/2

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  17. Solve dy/dx+y/x=sinx/x,y(0)=0

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  18. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

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  19. A figure consists of a semi-circle with a rectangle on its diameter. G...

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  20. Find the points on the curve y = x^2+1 which are nearest to the point ...

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