AP Calculus AB: 12.2.1 L'Hôpital's Rule and Indeterminate Products
This content explains how to handle indeterminate products, which need to be transformed into quotients before applying L’Hôpital’s Rule. It covers strategies to rewrite limits involving products like 0·∞ into a quotient form, enabling the use of derivatives to evaluate tricky limits.
L’Hôpital’s Rule and Indeterminate Products
Some indeterminate forms have to be transformed before you can apply L’Hôpital’s rule.
When applying L’Hôpital’s rule to an indeterminate product, express one of the factors as a fraction.
Key Terms
L’Hôpital’s Rule and Indeterminate Products
Some indeterminate forms have to be transformed before you can apply L’Hôpital’s rule.
When applying L’Hôpital’s rule to an ...
note
An example of a camouflaged indeterminate form is the indeterminate product 0 · . It is indeterminate because you cannot tell who wins. Zer...
Evaluate limx→∞xsin2/x
2
Evaluate limx→1 (x−1)^3(1−x)^−2.
0
Evaluate limx→∞ e^−x√x.
0
Evaluate limx→∞ x^−1e^x.
∞
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| Term | Definition |
|---|---|
L’Hôpital’s Rule and Indeterminate Products |
|
note |
|
Evaluate limx→∞xsin2/x | 2 |
Evaluate limx→1 (x−1)^3(1−x)^−2. | 0 |
Evaluate limx→∞ e^−x√x. | 0 |
Evaluate limx→∞ x^−1e^x. | ∞ |
Evaluate limx→0 2xcotx. | 2 |
Evaluate limx→0 1/xcotx | 1 |
Evaluate limx→0 xlnx. | 0 |
Evaluate limx→0 x^−2(x−3)^3. | −∞ |