12.2.1 L'Hôpital's Rule and Indeterminate Products Flashcards
1
Q
L’Hôpital’s Rule and Indeterminate Products
A
- 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.
2
Q
note
A
- 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.
3
Q
Evaluate limx→∞xsin2/x
A
2
4
Q
Evaluate limx→1 (x−1)^3(1−x)^−2.
A
0
5
Q
Evaluate limx→∞ e^−x√x.
A
0
6
Q
Evaluate limx→∞ x^−1e^x.
A
∞
7
Q
Evaluate limx→0 2xcotx.
A
2
8
Q
Evaluate limx→0 1/xcotx
A
1
9
Q
Evaluate limx→0 xlnx.
A
0
10
Q
Evaluate limx→0 x^−2(x−3)^3.
A
−∞
