00:01
In this question, we are asked to find the values of x, for which the function, the values of a for which the function f is continuous at every value of x.
00:09
First of all, note that each part of the function f is continuous by itself.
00:16
And the only point where discontinuity may come from is the point x equals 2, because that's where the function breaks, changes its definition.
00:28
So we need to find, therefore, we need to test.
00:31
For continuity only at one point at x equals 2.
00:35
And for a function to be continuous at a point, in our case at x equals 2, we want the limit as x approaches 2 from the left to be equal to the limit as x approaches 2 from the right and be equal to the actual value of the function at x equals 2.
00:55
Let's calculate each quantity separately.
00:59
The limit of f of x as x approaches 2 from the left, now let's look at the number of.
01:06
Line.
01:08
So here is x equals 2 and now we are approaching 2 from the left.
01:16
This means that x is less than 2.
01:20
And when x is less than 2, we are looking at the second line of the function and in this case f equals to 30.
01:28
So we are calculating the limit of 30.
01:31
And since it doesn't depend on x, this limit equals to 30.
01:35
Now let's calculate the limit of f when x when x is approaching 2 from the right.
01:44
In this case, we are approaching 2 from this direction...