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)
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1
Q

L’Hôpital’s Rule and Indeterminate Differences

A
  • 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
Q

note

A
  • 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
Q

Evaluatelimx→∞ (4√x^4 + x^3 – x).

A

1/4

4
Q

Evaluate limx→∞(3√x^3+x^2−x)

A

1/3

5
Q

Evaluate limx→0 (1/x – 1/ln(1 + x)).

A

−1/2

6
Q

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

A

−1/2

7
Q

Evaluate limc→1(2cc2+c−2−1c−1).

A

The limit does not exist.

8
Q

Evaluate limx→∞ (√x + 2 – √x).

A

0

9
Q

Evaluate limx→0 (1x – cot x)

A

0

10
Q

Evaluatelimx→∞(x5−1000x4).

A

11
Q

Evaluate limx→∞ (√9x2 + 2x − 3x).

A

1/3

12
Q

Evaluate limx→0 (1x – 1sinx).

A

0

13
Q

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

A

−1/2

14
Q

Evaluate limx→∞(√x2+3x−x).

A

3/2

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