Flashcards in 12.2.2 L'Hôpital's Rule and Indeterminate Differences Deck (14):
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
- 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.
Evaluatelimx→∞ (4√x^4 + x^3 – x).
Evaluate limx→0 (1/x – 1/ln(1 + x)).
Evaluate limx→2 (1/x − 2 – 1/ln(x − 1))
The limit does not exist.
Evaluate limx→∞ (√x + 2 – √x).
Evaluate limx→0 (1x – cot x)
Evaluate limx→∞ (√9x2 + 2x − 3x).
Evaluate limx→0 (1x – 1sinx).
Evaluate limx→0 ⎛⎜⎝1ln(x + √1 + x2) – 1ln(1 + x)⎞⎟⎠