00:01
Here, we're given f of x piecewise.
00:03
So it follows one function that happens to be a polynomial if x is less than zero, and follows another function if x is bigger than zero.
00:12
We're asked some details about the continuity of f.
00:15
So first off, how do we know that a, or f of x, is not continuous at x equals zero? so what we need to do is find what is the limit? and is that equal to the function value? so let's take the limit from the left.
00:34
So the limit as x approaches zero from the left of f of x, well, that means we're going to follow the curve when x is less than, because that's what from the left means slightly less than zero, which means negative.
00:49
So we're going to follow the top graph.
00:53
So if x is zero, the top graph will be four.
00:58
Now let's find the limit as x approaches zero from the right.
01:04
Just like before, we're going to say that this plus sign means it's to the right, meaning slightly bigger than zero.
01:12
So we're going to follow this graph.
01:15
If i plug in zero, i get zero.
01:18
So the limit from the left does not equal the limit from the right...