00:01
In this problem, we have been asked to determine whether the limit exists by first of all writing the function as a piecewise function.
00:09
So the function we have is x cubed divided by the absolute value of x.
00:16
So let's write this as a piecewise function.
00:19
We'll have x cubed divided by x if x is greater than 0, because whenever x is greater than 0, the absolute value of x is x.
00:28
X and it will be x cubed divided by negative x if x is less than 0.
00:34
And this is because whenever x is less than 0, the absolute value of x is negative x.
00:39
And this function is not defined when x is 0 because in that case we will end up with 0 cubed divided by the absolute value of 0, which is 0 divided by 0 and that is undefined.
00:50
So this is what we get.
00:52
So let's simplify this.
00:54
We end up with x squared when x is greater than 0 and negative x squared when x is less than 0...