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Show that the semi-vertical angle of the...

Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is `tan^-1sqrt2`.

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PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE
  1. Prove that volume of largest cone, which can be inscribed in a sphere,...

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  2. Show that the right circular cone of least curved surface and given vo...

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  3. Show that the semi-vertical angle of the cone of the maximum volume an...

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  4. Show that semi-vertical angle of right circular cone of given surface ...

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  5. The point on the curve x^2 = 2y which is nearest to the point (0,5) is...

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  6. For all real values of x, the minimum value of (1-x+x^2)/(1+x+x^2 is:

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  7. The maximum value of [x(x-1)+1]^(1/3), 0lexle1 is:

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  8. Using differentials, find an approximate value of each of the followin...

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  9. Using differentials, find an approximate value of each of the followin...

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  10. Show that the function given by f(x) = (logx)/x has maximum at x=e

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  11. The two equal sides of an isosceles triangle with fixed base b are dec...

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  12. Find the slope of the normal to curve xy = 6 at point (1,6)

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

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

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

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

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

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

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  19. A tank with rectangular base and rectangular sides, open at the top is...

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

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