00:01
All right, we're taking the limit as x goes to negative infinity, and we have a logarithm in here, so we're going to have to be careful that nothing crazy happens.
00:11
All right, so let's plug negative infinity in and see what happened.
00:14
Negative infinity to the fourth power.
00:17
Well, if you raise a negative to the fourth power, it's positive.
00:20
So positive infinity plus one, that's positive infinity.
00:25
Okay, the natural log looks like this.
00:29
So the log of infinity, that's way out here.
00:32
That's infinity so we get infinity over negative infinity okay that's an indeterminate form so we can use lopetal's rule so it's the limit as x goes to minus infinity take the derivative of the top and remember the derivative of the natural log of something is one over the something times the derivative of the something which is for x to the third power and that's all over the derivative of x, which is just one.
01:12
All right, so now plug minus infinity in there again, and you get minus infinity to the third power.
01:19
That's minus infinity times four...