
3-26 Calculus – Differentiation and Integration
In a similar fashion, we can derive the following definitions:
Definition 3.4 lim ( )
x
→+∞
=−∞ if and only if for every N > 0 there exists some M > 0 such that
f(x) < -N whenever x > M.
Definition 3.5 lim ( )
x
→−∞
= ∞ if and only if for every N > 0 there exists some M > 0 such that
f(x) > N whenever x < -M.
Definition 3.6
lim ( )
x
→−∞
=−∞ if and only if for every N > 0 there exists some M > 0 such that
f(x) < -N whenever x < -M.
Note 3.4 Though we use ¥ in our formulae, it is not a number.
Example 3.20 Evaluate lim .
x
x
→−∞
−
30
5
Solution: We observe that the numerator always remains 5. ...