4. •Function
- is a binary relation over two sets that associates
every element of the first set, to exactly one
element of the second set.
•Evaluating a Function
-Means replacing the variable in the function.
25. The analysis of the behaviour of a function as it
approaches some point (which may or may not be in
the domain of the function!).
This comes up in the real world all the time: any time
a model uses “ideal” conditions, we are looking at a
limit.
26. Is the value that a function (or sequence)
"approaches" as the input (or index) "approaches"
some value.
27. The fact that a function f approaches the
limit L as x approaches a is sometimes denoted by a
right arrow (→), as in:
28. When we evaluate a lim
𝑥→𝑎
𝑓(𝑥) we do one of the
following.
1. Find the limit value L in simplified form:
We write:
29. When we evaluate a lim
𝑥→𝑎
𝑓(𝑥) we do one of the
following.
2. When the limit is infinity (∞) or negative infinity
(−∞): We write:
30. When we evaluate a lim
𝑥→𝑎
𝑓(𝑥) we do one of the
following.
3. When the limit “Does Not Exist (DNE)” in some
other way,we write:
31. When we evaluate a lim
𝑥→𝑎
𝑓(𝑥) we do one of the
following.
If we say the limit is ∞ or −∞ , the limit is still not
exist. Think of ∞ or −∞ as “special cases of DNE”.
exists
The limit is a real number, L.
does not exist “DNE”
-
x a
