(a) Find the average rate of change of the area of a circle with respect to its radius as changes from (i) 2 to 3 (ii) 2 to 2.5 (iii) 2 to 2.1 (b) Find the instantaneous rate of change when . (c) Show that the rate of change of the area of a circle with respect to its radius (at any ) is equal to the circumference of the circle. Try to explain geometrically why this is true by drawing a circle whose radius is increased by an amount . How can you approximate the resulting change in area if is small?

Wesley Fowler ASTR Chapter 6 Nebular Theory The nebular theory claims that the existing solar system was formed by the collapse of a giant cloud of interstellar gas and dust. 1. A cloud of gas and dust (nebula) exists 2. The nebula is compressed (by gravity, shockwave) 3....