00:01
This question we want to find the limit as t approaches 0 of e to the negative 3ti plus t squared over sine squared of t times j plus the cosine of 2t times k.
00:13
So to do this we're just going to take the limit one component at a time.
00:18
In other words, i start by finding the limit as t approaches 0 of e to the negative 3t.
00:25
To evaluate this limit i plug in.
00:28
I'm getting e to the power of 0 which is 1.
00:33
Then i move to my second component.
00:36
The limit as t approaches 0 of t squared over the sine squared of t.
00:44
Now to do this i'm actually going to think of this a little differently.
00:50
I'm going to think of this as the limit as t approaches 0 of the quantity of t over the sine of t being squared.
01:01
Now that inside is a limit that you may have seen in the past.
01:07
The limit as t approaches 0 of t over the sine of t.
01:12
If you try direct substitution you get 0 over 0.
01:17
However, by applying l 'hopital's rule you get the limit as t approaches 0...