00:01
All right, so in this question we're asked to determine the limit as x goes to 0 of 1 minus 3, 1 minus cosine 3x divided by 2x.
00:14
All right, the first thing we can do, so what's assigned in red, we're going to try to simplify what we have inside the limit.
00:21
The first thing that we can do is multiply by a sneaky one, so we can multiply by 3 divided by 3.
00:30
And the reason for that is we'll see it in a while so if we multiply the numerator by 3 and the denominator by 3 what we can do is we can switch the we can take this 2 on the out put it on the outside and we put that 3 on the inside so you see i just switched that 3 and the 2 so we have 3 over 2 and then 1 minus cosine 3x divided by 3x all right so this is the simplification that we did.
01:05
And then now we're going to try to put that back into our limit.
01:11
So we copy what we did, the simplification, and then we put it back inside our limit.
01:16
So we get this right here.
01:19
All right.
01:19
Now, remember our rules for our limit, so that 3 divided by 2, 3 halves is a constant.
01:25
So you could pull it to the outside right here.
01:30
And then now let's look at this, the limit of 1 minus cosine 3 x...