00:01
Consider the graph of f below.
00:02
For this problem, we want to determine which among the statements may be false.
00:06
Let's look at the first one.
00:08
It says limit of f of x as x approaches to exists.
00:12
But the question is, when does the limit of a function as it approaches, let's say, a exists? well, we note that limit of f of x as x approaches a exists if limit of f of x is x approaches a from the left equals the limit of f of x is x approaches a from the right.
00:39
In other words, the graph of the function, either from the left or from the right, of the point whose x coordinate is a.
00:47
This point may be shaded or unshaded, will approach f of a.
00:53
So let's look at our graph and see if the first statement is true or false.
01:00
So limit of f of x as x approaches to exists because if you look at this point, which is our point of concern, either we look at the graph from the left side of this point or from the right side, they both approach the same point.
01:21
So this is true.
01:22
For part b, we look at the point on the graph with coordinate x equals 3, so this point.
01:30
And if you can see, as you move closer to this point, either from the left side or right side, they both approach to the same point.
01:39
So this is also true.
01:41
For part c, we look at the graph of f as x gets closer to 4.
01:46
So if you look at the left side, the graph is approaching this point, but for the right side, the graph is approaching this point.
01:57
So since the points are not the same, this limit does not exist...