00:01
Okay, so we want to evaluate this limit, the limit as t tends to two of t to the power 4 minus 62 t squared minus 3t plus 3 using the appropriate limit laws.
00:13
So the first thing we're going to do is because the limit of all of these exist, instead of taking the limit of this sum, we can take the sum of the limits.
00:23
So we're going to have to limit as t tends to two of t to the four minus 60, well actually let's leave it as limit as t tends to two of 62 t squared, minus the limit as t tends to two of three t, plus the limit as t tends to two of three.
00:50
Now for these with this constant in front, we can pull this eight side the limit.
00:54
So this becomes the limit as t tends to two of t to the power of four, minus 62 limit as, limit as t tends to two of t squared, minus three times the limit as t tends to two of t.
01:16
And then we can just evaluate this limit directly.
01:18
The limit as t tends to two of the constant three is just three.
01:22
So we have three on the end.
01:24
Okay, the next thing we're going to do is for these, the limit as t tends to 2 of t to the 4 is the same as the limit as t tends to 2 of t or to the power 4.
01:35
So we can in some sense bring this limit inside this power...