StudyXY
RegisterLog in
Back to AI Flashcard MakerMathematics /AP Calculus AB: 12.1.1 Indeterminate Forms

AP Calculus AB: 12.1.1 Indeterminate Forms

Mathematics14 CardsCreated 3 months ago

This content focuses on identifying and resolving indeterminate forms like 0/0 and ∞/∞ when evaluating limits. It explains algebraic strategies such as factoring and dividing by the highest power to simplify expressions and determine meaningful limit values.

PrintEmbedImportReport

Indeterminate Forms

  • A limit of a function is called an indeterminate form when it produces a mathematically meaningless expression. Two types of indeterminate forms are 0/0 and ∞/∞.

  • Some indeterminate forms can be solved by using algebraic tricks such as canceling or dividing by the highest power of x.

Tap or swipe ↕ to flip
Swipe ←→Navigate
1/14

Key Terms

Term
Definition

Indeterminate Forms

  • A limit of a function is called an indeterminate form when it produces a mathematically meaningless expression. Two types of indeterminate ...

note

  • When taking limits, sometimes you will encounter expressions whose meanings can be interpreted in different ways. These limits are called i...

Evaluate limx→∞ 4x5+10x3+9x2+2x+12x5−3x4−9x+5

2

Evaluate limx→3 x3−27x2−2x−3.

27/4

Evaluate limx→∞ 8x8−x5+x2+11−2x8

-4

Evaluate limx→100100x−x2x3−100x2.

-1/100

Log in to view all terms

Related Flashcard Decks

Mathematics

Essential SAT Math Formulas

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

10 cards
View Deck
Mathematics

Brain and Behavior Chapter 4: Neural Conduction & Synaptic Transmission Part 4

This deck covers key concepts from Chapter 4 of Brain and Behavior, focusing on neural conduction and synaptic transmission, including neurotransmitter deactivation, glial cell functions, and neurotransmitter classifications.

25 cards
View Deck
Mathematics

Behavioral Neuroscience Chapter 3 Test

This deck covers key concepts from Chapter 3 of Behavioral Neuroscience, focusing on the structure and function of the nervous system, including sensory neurons, brain regions, and neural techniques.

20 cards
View Deck
Mathematics

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.

29 cards
View Deck
Mathematics

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.

53 cards
View Deck
Mathematics

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.

55 cards
View Deck

Study Tips

  • Press F to enter focus mode for distraction-free studying
  • Review cards regularly to improve retention
  • Try to recall the answer before flipping the card
  • Share this deck with friends to study together
AP Calculus AB: 12.1.1 Indeterminate Forms
TermDefinition

Indeterminate Forms

  • A limit of a function is called an indeterminate form when it produces a mathematically meaningless expression. Two types of indeterminate forms are 0/0 and ∞/∞.

  • Some indeterminate forms can be solved by using algebraic tricks such as canceling or dividing by the highest power of x.

note

  • When taking limits, sometimes you will encounter expressions whose meanings can be interpreted in different ways. These limits are called indeterminate forms. 0/0 is one example.

  • One camp says that the indeterminate form equals one because it is a number divided by itself.

  • Another says that zero divided by anything is zero.

  • A third says that any number divided by zero is infinity.

  • Similar arguments hold for the form.

  • When an indeterminate form arises, you will have to do more work.

  • One algebraic trick involves factoring the numerator and the denominator.

  • In this case, you can cancel the (x – 3) factors as long as you promise not to let x be equal to three.

  • To evaluate this limit, look for the highest power.

  • In this case, x 3 is the highest power, so divide the numerator and denominator by it. You are essentially multiplying by a form of one.

  • Now all the terms have x in the denominator except one. Those terms will approach zero.

  • The result is not an indeterminate form. It is negative infinity

Evaluate limx→∞ 4x5+10x3+9x2+2x+12x5−3x4−9x+5

2

Evaluate limx→3 x3−27x2−2x−3.

27/4

Evaluate limx→∞ 8x8−x5+x2+11−2x8

-4

Evaluate limx→100100x−x2x3−100x2.

-1/100

Evaluate limx→2 x3−4x3x−6.

8/3

Evaluate limx→1 x12−2x11+x10x3−x2−x+1

1/2

Evaluate limx→∞ 2x3−33x3−4x2+1.

2/3

Evaluate limx→3 2x−6x2−4x+3.

1

Evaluate limx→∞ 2x2000−5x+4002x2001+2001

0

Evaluate limx→2 x3−2x210x−20

2/5

Evaluate limx→0 x3−3x211x5−4x2.

3/4

Evaluate limx→1 x2+2x−3x−1

4