00:01
Here we want to know the rate of change of the area of a circle with respect to the radius when the radius is r equals three.
00:07
So to find the rate of change, we're going to use our limit definition of a derivative.
00:10
We have the limit of h approaching zero of f.
00:14
We'll call this function f of r.
00:17
So f of r plus h minus f of r over h.
00:21
We'll just plug everything in.
00:23
So if we plug in r plus h, we'll have pi at times r plus h squared, minus we just plug in r is just pi r squared.
00:30
This is over h.
00:31
Let's expand out this r plus h squared.
00:33
So we have pi times r squared plus 2 rh plus h squared minus pi r squared and this is over h.
00:42
So we can actually get rid of this pi r squared because we also have a pi r squared here when this goes in.
00:49
So we can rewrite this as if we multiply the pi in.
00:54
Actually we could leave the pi all makes it just as convenient...