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Show that 2 sin x + than x ge 3x all x i...

Show that `2 sin x + than x ge 3x all x in (0, pi/20).

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MODERN PUBLICATION-SAMPLE PAPER 2015-EXERCISE
  1. Show that (dy)/(dx) is independent of t . cos x=sqrt((1)/(1+t^(2))) an...

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  2. Verify Euler's theorem in the case of z = xy+((x+y)^(4))/(xy).

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  3. Show that 2 sin x + than x ge 3x all x in (0, pi/20).

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  4. Find the following limits:lim(xrarr0+)logtanx tan2x

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  5. Find the approximate value of root(6)(63).

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  6. Evaluate : intx^(2)tan^(-1)xdx.

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  7. Evaluate int dx/(x ln (x)sqrt((In(x))^2-4))

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  8. Find the area of the circle x^2+y^2=2ax.

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  9. Find the particular solution ofthe differential equation (d^2y)/(dx^2)...

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  10. Solve the following differential equation (x+2y^(3))dy/dx=y.

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  11. Solve the following differential equation : x^(2)(y-1)dx+y^(2)(x-1)dy ...

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  12. Prove that the lines joining the midpoints of consecutive sides of a q...

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  13. Prove that : [(vec a × vec b) (vec b × vec c) (vec c × vec a)] = [vec ...

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  14. If vec a, vec b, vec c are mutually perpendicular vectors of equal mag...

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

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  16. Find the equation of the plane through the points (1, 2, -3), (2,3, -4...

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  17. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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  18. Solve the following LPP graphically : Minimize Z = 6x(1)+7x(2) Sub...

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  19. Find the feasible region the the following system of equations 2y-xge0...

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  20. Solve the following equations by cramer's rule : 7x+y+1 = 0, x+13y+5 =...

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