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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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NCERT TELUGU-APPLICATION OF DERIVATIVES-EXERCISE 6.6
  1. The two equal sides of an isoceles triangle with fixed base b are decr...

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  2. The equation of the normal to the curve x^(2)=4y at (1,2) is

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  3. Show that the normal at any point theta to the curve x = a cos theta +...

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  4. Find the intervals in which the function f given by f(x) = (4sin x-2...

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  5. Find the intervals in which the function f given by f(x) =x^(3) +(1)/(...

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  6. Find the maximum area of an isosceles triangle inscribed in the ellips...

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  7. A tank with rectangular base and rectangular side, open at the top is ...

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  8. The sum of the perimeter of a circle and square is k, where k is some ...

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  9. A window is in the form of a rectangle surmounted by a semi-circular o...

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  10. Find the points at which the function f given by f (x) = (x-2)^(4)(x+1...

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  11. Find the absolute maximum and minimum values of the function f given b...

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  12. Let f be a function defined on [a, b] such that f'(x)>0 for all x in ...

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

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

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

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

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  17. The line y = mx + 1 is a tangent to the curve y^(2)= 4x if the value o...

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

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  19. The equation of the normal to the curve x^(2)=4y at (1,2) is

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

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