12.1.4 More Exotic Examples of Indeterminate Forms Flashcards Preview

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

More Exotic Examples of Indeterminate Forms

A
  • 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
Q

note

A
  • 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
Q

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

A

Finding the derivative of (2x)

4
Q

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

A

limx→0 87x3+6sinx+10

5
Q

Evaluate limx→∞ 2x+5ex.

A

0

6
Q

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

A

The limit is equal to 1

7
Q

Evaluate limx→0cos(10x)−110x

A

0

8
Q

Evaluate limx→0sin2xcosx−1

A

−2

9
Q

Evaluate limx→0 1/sinx.

A

The limit does not exist.

10
Q

Evaluate limx→0 cos2x−1/sinx

A

0

11
Q

Evaluate limx→∞(lnx)+3/2−x3

A

0

12
Q

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

A

b

13
Q

Evaluate limx→−∞ x4/e−x

A

0

14
Q

Evaluate limx→π/2 sinx+cosx−1/cosx

A

1

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