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The given quantity of metal is to be cos...

The given quantity of metal is to be cost into a half cylinder with a rectangular base and semicircular ends. Show that in order that the total surface area may be minimum, the ratio of the length of the cylinder to the diameter of its semi-circular ends is `pi:(pi+2)dot`

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RD SHARMA ENGLISH-MAXIMA AND MINIMA-All Questions
  1. Find dy/dx if x+y = e^y+sinx

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  2. The sum of the surface areas of a sphere and a cube is given. Show tha...

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  3. The given quantity of metal is to be cost into a half cylinder with a ...

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  4. Find dy/dx if y = x.siny

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  5. A straight line is drawn through a given point P(1,4)dot Determine the...

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  6. The total area of a page is 150c m^2dot The combined width of the marg...

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  7. The space s described in time t by a particle moving in a straight ...

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  8. A particle is moving in a straight line such that its distance s at an...

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  9. Write necessary condition for a point x=c to be an extreme point ...

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  10. Write sufficient conditions for a point x=c to be a point of local ...

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  11. If f(x) attains a local minimum at x=c , then write the values of ...

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  12. Write the minimum value of f(x)=x+1/x ,\ \ x >0

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  13. Write the maximum value of f(x)=x+1/x ,\ \ x<0 .

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  14. Write the point where f(x)=x\ (log)e x attains minimum value.

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  15. Find the least value of f(x)=a x+b/x , where a >0,\ \ b >0 and x >0...

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  16. Write the minimum value of f(x)=x^x .

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  17. Write the maximum value of f(x)=x^(1//x) .

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  18. Write the maximum value of f(x)=(logx)/x , if it exists.

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  19. The maximum value of x^(1/x),x &gt;0 is (a)e^(1/e) (b) (1/e)^e (c)...

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  20. If a x+b/xgeqc for all positive x where a ,\ b ,\ >0 , then a b<(c^2)/...

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