Explain why the function is discontinuous at the given number a = 1 ?
2 Answers
The limit of the first piece as x approaches 1 from the negative side is:
We do need to take a limit for the second piece; we can just evaluate it at 1:
The function is discontinuous because the two pieces do not have the same y value at 1;
See below
Explanation:
To show that
In this case
Now let's consider
In this case
So as
Since
[NB: