00:01
So in this question, we have a rather complicated looking limit, and we want to estimate this limit using grabs or tables.
00:09
I have a limit as x approaches 1 of the square root of 2x minus x to the 4th, minus the cube of x all over 1 minus x to the 11 4th power.
00:22
And what i'm going to do is i'm going to make a graph this time.
00:27
So let's see here.
00:28
I'm going to go to my calculator and this is pretty complicated.
00:32
So i'm going to do this in a couple of pieces so i don't mess up the parentheses.
00:37
In y1, i'm just going to put my numerator.
00:41
The square root of 2x minus x to the fourth and from this i am subtracting the cube root of x.
00:57
And then in my y2 i'm going to put my denominator.
01:00
So my denominator is 1 minus x to the power of 11 quarters.
01:09
Now once i have y1 and y2, i'm going to make the function that i'm interested in by taking the quotient y1 over y2.
01:20
So alpha trace y1 over y2.
01:26
Now i'm going to turn the graphs of y1 and y2 off so that i don't see them.
01:34
And i'm going to make this graph.
01:37
I'm going to go back to a standard viewing window.
01:40
And it's a little tricky to see what's going on here, right? so i'm going to zoom in a little closer to the origin.
01:49
And then i'm going to zoom in a little closer to this point where x is equal to one.
02:01
So i'm trying to zoom in here on the point where x is equal to one.
02:08
And if i zoom in yet again, let's see what we're getting.
02:14
Okay...