Register Log in

Mathematics /AP Calculus AB: 12.2.2 L'Hôpital's Rule and Indeterminate Differences

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

Mathematics14 CardsCreated 7 months ago

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.

Print Embed Import Report

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

Rate to track your progress ✦

Tap to flipTap or swipe ↕ to flip

Space↑↓

←→Swipe ←→Navigate

SSpeak

FFocus

1/14

Key Terms

Term

Definition

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

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

Related Flashcard Decks

Functions and Their Properties

This deck covers various types of functions, including polynomial, rational, exponential, piecewise, and composite functions, as well as transformations like shifts of graphs and concepts like difference quotients.

Hungarian Assignment Method and Assignment Problems

This deck covers key concepts related to the Hungarian Assignment Method and the Assignment Problem, including optimal solutions, effects on cost tables, and objectives in different cases.

Functions and Principles of the Human Rights Commission

This deck covers the functions and guiding principles of the Human Rights Commission as outlined in the charter, focusing on protection, research, dissemination, and collaboration efforts.

Frege Concepts and Analysis

This flashcard deck covers key concepts and analyses related to Frege's work, including definitions, relationships, and important facts.

FRACTIONS VOCABULARY STUDY GUID TEST ON FRIDAY JANUARY 16TH

THIS IS A GOOD FLASH CARD GAME TO PRACTICE

Essential SAT Math Formulas

This deck covers key formulas and concepts essential for the SAT Math section, including slope, distance, and vertex forms.

Algebra 1 Unit 1 Mastery Test

These properties of equality help maintain balance in an equation when performing the same operation on both sides. Inverse operations, like using addition to undo subtraction, are key tools in solving equations.

ATI TEAS Test Practice Mathematics Part 2

This flashcard set includes a variety of practical math questions covering percentages, conversions, averages, scale drawings, and basic algebra. It’s designed to strengthen problem-solving skills for real-life and standardized test situations.

ATI TEAS Test Practice Mathematics Part 1

This flashcard set includes a variety of practical math questions covering percentages, conversions, averages, scale drawings, and basic algebra. It’s designed to strengthen problem-solving skills for real-life and standardized test situations.

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

Term	Definition
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
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.
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
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