12.1.4 More Exotic Examples of Indeterminate Forms Flashcards Preview

AP Calculus AB > 12.1.4 More Exotic Examples of Indeterminate Forms > Flashcards

Flashcards in 12.1.4 More Exotic Examples of Indeterminate Forms Deck (14):
1

More Exotic Examples of Indeterminate Forms

• As long as the limit still produces an indeterminate form, you can reuse L’Hôpital’s rule.
• When applying L’Hôpital’s rule to a quotient containing one or more products or compositions of functions, it is necessary to use the product or chain rules.
• L’Hôpital’s rule might not give you the right answer if you use it on a limit that does not produce an indeterminate form.

2

note

- Some limits produce an indeterminate form that cannot be eliminated by factoring. In these cases, L’Hôpital’s rule is very useful.
- These two limits are classic limits that may appear in other situations, such as the limit definition of the derivative for trig functions.
- To apply L’Hôpital’s rule, you will need to remember the derivatives of sin x and cos x.
- This limit does not meet the criteria for L’Hôpital’s rule because it does not produce an indeterminate form. If you tried to use L’Hôpital’s rule here, you would get a different answer.
- In a complicated limit it can be helpful to think about the behavior of specific terms. In this example, the 3 has a negligible effect. The x-squared term in the numerator will overpower x ln x in the denominator.
- After using L’Hôpital’s rule once, the limit produces an indeterminate form again. A second application results in an answer.
- You can say the limit is infinity, but since that is not a number you can also say that it does not exist.

3

Which of the following is not a step when L'Hôpital's rule is used to determine limx→2 x2−x−2/x−2?

Finding the derivative of (2x)

4

Which of the following limits does not produce an indeterminate form?

limx→0 87x3+6sinx+10

5

Evaluate limx→∞ 2x+5ex.

0

6

Which of the following statements about this limit expression is not correct?
limx→0 tanx/2x

The limit is equal to 1

7

Evaluate limx→0cos(10x)−110x

0

8

Evaluate limx→0sin2xcosx−1

−2

9

Evaluate limx→0 1/sinx.

The limit does not exist.

10

Evaluate limx→0 cos2x−1/sinx

0

11

Evaluate limx→∞(lnx)+3/2−x3

0

12

How many times is L'Hôpital's rule used to solve for limx→∞ xb/ex, where b is a positive integer?

b

13

Evaluate limx→−∞ x4/e−x

0

14

Evaluate limx→π/2 sinx+cosx−1/cosx

1

Decks in AP Calculus AB Class (190):