Flashcards in 12.2.1 L'Hôpital's Rule and Indeterminate Products Deck (10):
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.
- An example of a camouflaged indeterminate form is the indeterminate product 0 · . It is indeterminate because you cannot tell who wins. Zero times anything is zero, but anything times infinity is infinity, so what is the limit?
- If you write as , then your limit produces the standard
indeterminate quotient L’Hôpital’s rule. , which allows you to use
- This limit also produces the indeterminate product 0
- Here, it makes sense to write cot θ as the reciprocal of tan θ. Then you have the other standard indeterminate quotient, 0/0.
Evaluate limx→1 (x−1)^3(1−x)^−2.
Evaluate limx→∞ e^−x√x.
Evaluate limx→∞ x^−1e^x.
Evaluate limx→0 2xcotx.
Evaluate limx→0 1/xcotx
Evaluate limx→0 xlnx.