PLEASE SHOW YOUR SOLUTION.

Exercise 2.3 Rate of Change Solve the following problems. 1. Find how fast the area of a triangle increases as the length of the base of the triangle increases with a fixed height of 3 cm. 2. Find how fast the volume of a sphere increases as the radius also increases. 3. Find how fast the surface area of a sphere increases as the radius also increases when r = 6 inches. 4. Find how fast the area of a square increases when its side is 4 units. 5. Find how fast the volume of a cube increases as the dimension of the side also increases. 6. Find the rate of change of the total surface area of a right circular cylinder with a fixed height of 20 cm with respect to the radius. 7. Find the rate of change of the area of an ellipse with respect to the major axis. 8. Find how fast the lateral surface area of a right circular cylinder increases as the radius also increases when the altitude is 4 inches. 9. Find the rate of change of the area of an equilateral triangle with respect to its side. 10. Find the rate of change of the ordinate of the curve y = x + 3x -1 with respect to the abscissa at point (1,3)