Absolute value limit? (should be easy)
Heres the question and answer:
find the limit x -> -2 for the function:
So I graphed it out and saw
a gap where x -> -2 and so I said the limit does not exist,
which is correct according to the textbook. But the
textbook solves the question in a way I'm not familiar with
could someone please explain whats happening here?
t-> -2 from the left =
- (x + 2)
_______ = -1
x + 2
t-> -2 from the right =
(x + 2)
______ = 1
x + 2
Algebraically it makes sense to me, however I thought that I had to use direct substitution to get the answer, in which case it makes no sense to me.
Also, why does the absolute value become replaced with a negative sign when coming from the left. Is this a general rule I can apply to these types of questions?
Normally I would look at other questions in the book like this one, but this is the only one from the questions with absolute value.