00:01
For this problem, we want to find the instantaneous velocity of an object after three seconds, given that its position is defined by s of t, which is equal to t squared plus 2t.
00:12
Now, when we say instantaneous velocity, this is velocity v of t, which is equal to s primate t.
00:20
So since velocity of an object at time t equals a, it's given by v of a, that's equal to s prime of a, which is also the limit as t approaches a of s of s of a over t minus a, then when a is equal to 3, we have v of 3 equal to the limit as t approaches a of s of s of a over t minus a, then when a is equal to 3, we have v of 3 equal to the limit as t approaches 3 of s of t, that's t squared plus 2t minus.
01:00
We have s of 3, that'll be 3 squared plus 2 times 3, all over t minus 3.
01:09
This gives us limit as t approaches 3 of t squared plus 2t minus 15, all over t minus 3.
01:21
This gives us limit as t approaches 3 of t minus 3 times t plus 5 all over t minus 3...