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Show that semi-vertical angle of righ...

Show that semi-vertical angle of right circular cone of given surface area and maximum volume is `sin^(-1)(1/3)` .

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BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. A sheet of area 40m^2 is used to make an open tank with square base. F...

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  2. A right circular cylinder of maximum volume is inscribed in a given ri...

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  3. Show that semi-vertical angle of right circular cone of given surfa...

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  4. If the sum of the lengths of the hypotenuse and another side of a righ...

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  5. Find the point (alpha,beta) on the ellipse 4x^2+3y^2=12 , in the first...

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  6. A rectangle is inscribed in an equilateral triangle of side length 2a ...

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  7. Tangents are drawn to x^2+y^2=16 from the point P(0, h)dot These tange...

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  8. f(x)=x^(1/5) at x=0 has inflection point. y"\ DdotNdotEdot\ at x=0

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  9. f(x)=x^3a t\ x=0 has inflection point y ' '=0 at x=0 and change sign.

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  10. f(x)=|x^2-1| has no inflection point in its domain as no tangent ca...

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  11. Number of points of inflection for f(x)=x^2e^(-|x|) is 1 (b) 2 (...

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  12. Find the value of a if x^3-3x+a=0 has three distinct real roots.

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  13. Prove that there exist exactly two non-similar isosceles triangles A B...

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  14. Find the set of value of m for the cubic x^3-3/2x^2+5/2=(log)(1/4)(...

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  15. The set of value(s) of a for which the function f(x)=(a x^3)/3+(a+2)x^...

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  16. The number of values of k for which the equation x^3-3x+k=0 has two di...

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  17. Find the shortest distance between the curves y^2=x^3a n d\ 9x^2+9y...

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  18. let f(x)=-x^3+(b^3-b^2+b-1)/(b^2+3b+2) if x is 0 to 1 and f(x)=2x-3 if...

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  19. If the function f(x)=(a+3)x^3+(a-3)x^2+4(a-4)x+5 has maxima at some x...

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  20. Find a point M on the curve y=3/(sqrt(2))\ \ xlnx ,\ x\ in (e^(-1. 5)...

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