Barrons AP Calculus - David Bock

EXAMPLE 5

Describe the behavior of near x = 1 using limits.

SOLUTION: The graph (Figure N2–5) shows that:

FIGURE N2–5

Remember that none of the limits in Examples 4 and 5 exists!
DEFINITION
We write

if the difference between f (x) and L can be made arbitrarily small by making x sufficiently large
positively (or negatively).
In Examples 4 and 5, note that
EXAMPLE 6
From the graph of (Figure N2–6), describe the behavior of h using limits.
SOLUTION: