00:01
Let's suppose i'm taking the limit as x is a protein positive, but as the x values are increasing of a quadratic function over a cubic function.
00:09
So let's look at the end behavior of each of these functions first.
00:12
Let's try to evaluate this without using any sort of rule.
00:16
So my numerator is a quadratic function that opens up because the leading coefficient is positive.
00:22
So this means as my x values are increasing, my y values are also increasing in a positive way, or approaching positive infinity.
00:30
And then looking at my denominator, now this is a cubic function with a positive leading coefficient.
00:35
Okay, so it looks like so.
00:37
As my x values are increasing, my y values are also increasing in a positive way.
00:41
The question is, which infinity is bigger, or are they growing at the same rate? i could probably make a prediction here based on a quadratic versus a cubic function, but i'm going to use the lopitiles rule here just to confirm.
00:55
Lopetal's rule, i can take the derivative, of the top and bottom since i have the indeterminate of form infinity over infinity.
01:01
Derivative of the top, bring down the two, subtract one from the exponent.
01:05
Divid of seven is zero over two times three is six...