AP Calculus AB: 12.2.2 L'Hôpital's Rule and Indeterminate Differences
This content discusses transforming indeterminate differences into quotients by finding common denominators or factoring, enabling the application of L’Hôpital’s Rule. It explains the use of multiple rule applications and derivative techniques like the chain rule to resolve complex limits involving differences.
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
Key Terms
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 cl...
note
This is an example of an indeterminate difference that you can transform by finding a common denominator.
Once you have expr...
Evaluatelimx→∞ (4√x^4 + x^3 – x).
1/4
Evaluate limx→∞(3√x^3+x^2−x)
1/3
Evaluate limx→0 (1/x – 1/ln(1 + x)).
−1/2
Evaluate limx→2 (1/x − 2 – 1/ln(x − 1))
−1/2
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| Term | Definition |
|---|---|
L’Hôpital’s Rule and Indeterminate Differences |
|
note |
|
Evaluatelimx→∞ (4√x^4 + x^3 – x). | 1/4 |
Evaluate limx→∞(3√x^3+x^2−x) | 1/3 |
Evaluate limx→0 (1/x – 1/ln(1 + x)). | −1/2 |
Evaluate limx→2 (1/x − 2 – 1/ln(x − 1)) |
|
Evaluate limc→1(2cc2+c−2−1c−1). | The limit does not exist. |
Evaluate limx→∞ (√x + 2 – √x). | 0 |
Evaluate limx→0 (1x – cot x) | 0 |
Evaluatelimx→∞(x5−1000x4). | ∞ |
Evaluate limx→∞ (√9x2 + 2x − 3x). | 1/3 |
Evaluate limx→0 (1x – 1sinx). | 0 |
Evaluate limx→0 ⎛⎜⎝1ln(x + √1 + x2) – 1ln(1 + x)⎞⎟⎠ | −1/2 |
Evaluate limx→∞(√x2+3x−x). | 3/2 |