00:01
In this question, we are given a piecewise defined function, which depends on a parameter a.
00:07
And we're asked to choose to find the value of the parameter a, which makes this function continuous.
00:14
So i recall that the function is continuous, is the limit of f of x as x goes to a.
00:23
Sorry, in our case it's going to be as x goes to 0 is equal to f of 0.
00:29
In this case, our function is continuous at zero.
00:36
So basically, we want to find the value of a, which makes this limit is equal to the value to f of 0.
00:45
But first, let's find f of zero.
00:48
So to find f of zero, we need to follow the definition of the function.
00:52
And it says that for x greater equal than zero, we need to use the formula cosine x plus a.
01:01
And zero is included in this interval, right? because it is greater equal than zero.
01:06
Therefore, we have to use the second row to find the value of f of zero.
01:10
We're going to get cos 0 plus a.
01:14
And since cos 0 is equal to 1, we're going to get a plus 1.
01:19
So f of 0 is equal to a plus 1.
01:21
Good.
01:22
Now we need to find the limit of f of x as x goes to 0.
01:29
Limit as x goes to 0 of f of x.
01:35
And here we have to specify that we're going to zero from the left, if you're going to 0 from the left, this means that x is slightly less than 0 and we are going to use the first row...