00:01
So a horizontal asymptote occurs when x is going towards infinity or positive infinity, that's or infinity or negative infinity.
00:11
That's where we're going to get horizontal asymptotes.
00:13
Since it would be y is equal to some value and so it's going to be as x goes towards infinity, y is going towards some value.
00:20
So in order to find these horizontal asymptotes, we can look at the limit as x goes to infinity of our function 2x cubed plus 5x squared.
00:31
Divided by 3x cubed minus 1.
00:34
And so we can see that this is an infinity divided by infinity limit.
00:38
If we tried to directly substitute an x is equal to infinity, and so we can say this is equal to the limit as x goes to infinity of the derivative of the numerator, which is the derivative of 2x to the third power, which is just a power rule derivative.
00:53
So that's going to be 6x squared, then plus the derivative of 5x squared, which is 10x, and then divided by the derivative of the derivative of the, denominator, which is going to be 9x squared.
01:06
And so we can already factor out an x in the numerator, so we can get x times 6x plus 10 divided by 9x squared...