(a)
(b)
(c)
(d)
Although all indeterminate forms are listed above, only the indeterminate forms
are tested on both the AP Calculus AB and AP Calculus BC exams.
To find the limit of an indeterminate form of the type , we apply
L’Hôpital’s Rule, which involves taking derivatives of the functions in the
numerator and denominator. In the following, a is a finite number. The rule has
several parts:
If exists*, then
if does not exist, then L’Hôpital’s Rule cannot be applied.
If the same consequences follow as in case (a). The
rules in (a) and (b) both hold for one-sided limits.
If exists, then
if does not exist, then L’Hôpital’s Rule cannot be applied. (Here
the notation “x → ∞” represents either “x → +∞” or “x → −∞.”)
If , the same consequences follow as in case (c).
In applying any of the above rules, if we obtain again, we can apply the
rule once more, repeating the process until the form we obtain is no longer
indeterminate.
Example 38 __
is of type and thus equals .
(Compare with Example 12, in Chapter Two.)