Barrons AP Calculus - David Bock

EXAMPLE 40

(Example 13) is of type and thus equals as before. Note that is not

the limit of an indeterminate form!

EXAMPLE 41

is of type and therefore equals

EXAMPLE 42

(Example 20) is of type so that it equals which is again of type

Apply L’Hôpital’s Rule twice more:

For this problem, it is easier and faster to apply the Rational Function Theorem!

EXAMPLE 43

Find

SOLUTION: is of type and equals

EXAMPLE 44

Find

SOLUTION:

BEWARE: L’Hôpital’s Rule applies only to indeterminate forms Trying to use it in

other situations leads to incorrect results, like this:

L’Hôpital’s Rule can be applied also to indeterminate forms of the types 0 · ∞ and ∞ − ∞, if the
forms can be transformed to either

EXAMPLE 45

Find

SOLUTION: is of the type ∞ · 0. Since x and, as x → ∞, the latter is the

indeterminate form we see that