Flashcards in 12.1.4 More Exotic Examples of Indeterminate Forms Deck (14):
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.
- 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.
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)
Which of the following limits does not produce an indeterminate form?
Evaluate limx→∞ 2x+5ex.
Which of the following statements about this limit expression is not correct?
The limit is equal to 1
Evaluate limx→0 1/sinx.
The limit does not exist.
Evaluate limx→0 cos2x−1/sinx
How many times is L'Hôpital's rule used to solve for limx→∞ xb/ex, where b is a positive integer?
Evaluate limx→−∞ x4/e−x