12.2.2 L'Hôpital's Rule and Indeterminate Differences Flashcards Preview

AP Calculus AB > 12.2.2 L'Hôpital's Rule and Indeterminate Differences > Flashcards

Flashcards in 12.2.2 L'Hôpital's Rule and Indeterminate Differences Deck (14):
1

L'Hôpital's Rule and Indeterminate Differences

• Some indeterminate forms have to be transformed before you can apply L’Hôpital’s rule.
• Look for a common denominator or a clever way of factoring to transform an indeterminate difference into an indeterminate quotient to which you can apply L’Hôpital’s rule

2

note

- This is an example of an indeterminate difference that you can transform by finding a common denominator.
- Once you have expressed the limit as quotient, it produces the standard indeterminate form 0/0.
- A second application of L’Hôpital’s rule is needed since the limit produces an indeterminate form again.
- This limit produces an indeterminate difference, but it’s not obvious how to find a common denominator.
- Try factoring the expression, being very careful when working under the radical.
- Once you have factored out x, you can send it to the
denominator by finding its reciprocal,
- Now you have a limit that produces the form
apply L’Hôpital’s rule. , so you can
- The numerator includes a square-root expression, so you’ll have to use the chain rule.
- Cancel common factors and plug in the value to determine the limit.

3

Evaluatelimx→∞ (4√x^4 + x^3 – x).

1/4

4

Evaluate limx→∞(3√x^3+x^2−x)

1/3

5

Evaluate limx→0 (1/x – 1/ln(1 + x)).

−1/2

6

Evaluate limx→2 (1/x − 2 – 1/ln(x − 1))

−1/2

7

Evaluate limc→1(2cc2+c−2−1c−1).

The limit does not exist.

8

Evaluate limx→∞ (√x + 2 – √x).

0

9

Evaluate limx→0 (1x – cot x)

0

10

Evaluatelimx→∞(x5−1000x4).

11

Evaluate limx→∞ (√9x2 + 2x − 3x).

1/3

12

Evaluate limx→0 (1x – 1sinx).

0

13

Evaluate limx→0 ⎛⎜⎝1ln(x + √1 + x2) – 1ln(1 + x)⎞⎟⎠

−1/2

14

Evaluate limx→∞(√x2+3x−x).

3/2

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