Derivative as a rate measure

Derivative as a rate measure

Exercise 13.1

1. Find the rate of change of the total surface area of a cylinder of radius r and height h, when the radius varies.

Sol :

 

2. Find the rate of change of the volume of a sphere with respect to its diameter.

Sol :

 

3. Find the rate of change of the volume of a sphere with respect to its surface area when the radius is 2cm.

Sol :

 

4. Find the rate of change of the area of a circular disk with respect to its circumference when radius is 3cm.

Sol :

 

5. Find the rate of change of the volume of a cone with respect to the radius of its base.

Sol :

 

6. Find the rate of change of a circle with respect to its radius r when r=5cm.

Sol :

 

7. Find the rate of change of the volume of a ball with respect to its radius r. How fast is the volume changing with respect to the radius when the radius is 2cm.

Sol :

 

8. The total cost C (x) associated with the production of x units of an item is given by  C~(x) = 0.007x^3-0.003x^2+15x+4000 . Find the marginal cost when 17 units are produced.

Sol :

 

9. The total revenue received from the sale of x units of a product is given by  R (x)=13x^2+26x+15 . Find the marginal revenue when x = 7 .

Sol :

 

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