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Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle `alpha` is one-third that of the cone and the greatest volume of cylinder is `4/27 pi h^3 tan^2 alpha`

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PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE
  1. Let f be a function defined on [a, b] such that f'(x)>0 for all x in ...

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  2. Show that the height of the cylinder of maximum volume that can be ins...

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  3. Show that height of the cylinder of greatest volume which can be inscr...

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  4. A cylindrical tank of radius 10 m is being filled with wheat at the ra...

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  5. The slope of the tangent to the curve x = t^2+3t-8, y = 2t^2-2t-5at th...

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  6. The line y = mx +1, is a tangent to the curve y^2 = 4x if the value of...

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  7. The normal at the point (1,1) on the curve 2y + x^2 = 3 is:

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  8. The normal to the curve x^2 = 4y passing (1,2) is:

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  9. The points on the curve 9y^2 = x^3 , where the normal to the curve mak...

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  10. The rate of change of the volume of a sphere w.r.t. its surface area, ...

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  11. Fill in the blanks: Derivative of sin x w.r.t cos x is …………… .

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  12. Fill in the blanks: The side (Variable) of a square is x, then the r...

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  13. Fill in the blanks: The slope of the tangent to the curve y^2 = x^3 ...

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  14. Fill in the blanks: The function f(x) = x^3 is a strict function.

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  15. Fill in the blanks: The tangent to the curve y = x^3 at the point (4...

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  16. Fill in the blanks: When 0 l a<1,x>0, the function y = loga x is a ...

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  17. At x = 0, the function f(x) = |x| is

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  18. The values of a for which y=x^(2)+ax+25 touches the axis of x are .......

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  19. Fill in the blanks: The function f(x) = x + (9)/(x) has a local val...

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  20. Fill in the blanks: An approximate value of sqrt(66) is .

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