00:01
So to find a rate, that's the change in kulams over the change in time, and we're interested in that rate at three seconds.
00:08
So we'll take the limit as h approach at zero of our function evaluated at 3 plus h minus our function evaluated at 3, all divided by h.
00:20
So plugging in 3 plus h, we get one third, three plus h cubed, plus 3 plus h.
00:26
We'll then subtract our function evaluated at 3, all divided by h.
00:33
So probably the hardest part of this problem is just expanding 3 plus h cubed.
00:38
So let's do that just as a side step here.
00:42
3 plus h times 3 plus h is 9 plus 6h plus h squared.
00:47
Now we need to multiply that trinomial by the binomial 3 plus h.
00:51
We get 27, 18h, 3h squared.
00:56
And then multiplying by h, we get 9h, 6h squared, and h cubed.
01:01
So combining like terms, we get 20.
01:03
27, 27h, 9h squared, and h cubed.
01:09
So let's go back to our problem.
01:11
We have the limit as h approach is zero.
01:14
We need to take a third of those quantities.
01:16
So we'd have nine, nine h, three h squared, and a third of h cubed.
01:25
Then we have plus three plus h.
01:29
In the next set of brackets, we have three cubed, which is 27 times a third is nine, plus three is 12.
01:38
So let's see.
01:39
9 plus 3, you would notice is 12, minus 12, those cancel.
01:44
And all the terms left have an h in common.
01:48
So we can factor out that h and divide...