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A rectangle is inscribed in a semi-circl...

A rectangle is inscribed in a semi-circle of radius 'r' with one of its sides on diameter of semi-circle. Find the dimensions of the rectangle so that its area is maximum. Find also the area.

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MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
  1. Show that rectangle of maximum perimeter, which can be inscribed in a ...

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  2. Show that of all rectangles inscribed in a given circle the square has...

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  3. A rectangle is inscribed in a semi-circle of radius 'r' with one of it...

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  4. Of all rectangles , each of which has perimeter: 40 cm . Find the one ...

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  5. Of all rectangles , each of which has perimeter: 60 cm . Find the one ...

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  6. An open box with a square base is to be made out of a given iron sheet...

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

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  8. Show that the semi-vertical angle of the right-circular cone of maximu...

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  9. Prove that the semi-vertical angle of the right circular cone of given...

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

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  11. Show that the volume of the greatest cylinder, which can be inscribed ...

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  12. Show that the altitude of the right circular cone of maximum volume th...

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  13. Prove that volume of largest cone, which can be inscribed in a sphere,...

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

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

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  16. Show that the radius of right circular cylinder of maximum volume, tha...

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  17. Prove that the radius of the right-circlar cylinder of greatest curved...

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  18. Of all the closed cylindrical cans (right-circular). Which enclose a g...

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  19. Show that the surface area of a closed cuboid with surface base and gi...

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

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