The Limit Laws, Part I (2.1.4) Flashcards
1
Q
• Since limits are just numbers, a lot of the properties of real numbers also apply to limits.
A
• Since limits are just numbers, a lot of the properties of real numbers also apply to limits.
- An Introduction to Thinkwell Calculus (1.1.1)
- The Two Questions of Calculus (1.1.2)
- Average Rates of Change (1.1.3)
- How to Do Math (1.1.4)
- Functions (1.2.1)
- Graphing Lines (1.2.2)
- Parabolas (1.2.3)
- Some Non-Euclidean Geometry (1.2.4)
- Finding Rate of Change over an Interval (2.1.1)
- Finding Limits Graphically (2.1.2)
- The Formal Definition of a Limit (2.1.3)
- The Limit Laws, Part I (2.1.4)
- The Limit Laws, Part II (2.1.5)
- One-Sided Limits (2.1.6)
- The Squeeze Theorem (2.1.7)
- Continuity and Discontinuity (2.1.8)
- Evaluating Limits (2.2.1)
- Limits and Intermediate Forms (2.2.2)
- Two Techniques for Evaluating Limits (2.2.3)
- On Overview of Limits (2.2.4)
- Rates of Change, Secants, and Tangents (3.1.1)
- Finding Instantaneous Velocity (3.1.2)
- The Derivative (3.1.3)
- Differentiability (3.1.4)
- The Slope of a Tangent Line (3.2.1)
- Instantaneous Rate (3.2.2)
- The Equation of a Tangent Line (3.2.3)
- More on Instantaneous Rate (3.2.4)
- The Derivative of the Reciprocal Function (3.3.1)
- The Derivative of the Square Root Function (3.3.2)
- A Shortcut for Finding Derivatives (4.1.1)
- A Quick Proof of the Power Rule (4.1.2)
- Uses of the Power Rule (4.1.3)
- The Product Rule (4.2.1)
- The Quotient Rule (4.2.2)
- An Introduction to the Chain Rule (4.3.1)
- Using the Chain Rule (4.3.2)
- Combining Computational Techniques (4.3.3)
- A Review of Trigonometry (5.1.1)
- Graphic Trigonometric Functions (5.1.2)
- The Derivatives of Trigonometric Functions (5.1.3)
- The Number Pi (5.1.4)
- Graphing Exponential Functions (5.2.1)
- Derivatives of Exponential Functions (5.2.2)
- Evaluating Logarithmic Functions (5.3.1)
- The Derivative of the Natural Log Function (5.3.2)
- Using the Derivative Rules with Transcendental Functions (5.3.3)
- An Introduction to Implicit Differentiation (6.1.1)
- Finding the Derivative Implicitly (6.1.2)
- Using Implicit Differentiation (6.2.1)
- Applying Implicit Differentiation (6.2.2)
- The Exponential and Natural Log Functions (6.3.1)
- Differentiating Logarithmic Functions (6.3.2)
- Logarithmic Differentiation (6.3.3)
- The Basics of Inverse Functions (6.3.4)
- Finding the Inverse of a Function (6.3.5)
- Derivatives of Inverse Functions (6.4.1)
- The Inverse Sine, Cosine, and Tangent Functions (6.5.1)
- The Inverse Secant, Cosecant, and Cotangent Functions (6.5.2)
- Evaluating Inverse Trigonometric Functions (6.5.3)
- Derivatives of Inverse Trigonometric Functions (6.6.1)
- Defining the Hyperbolic Functions (6.7.1)
- Hyperbolic Identities (6.7.2)
- Derivatives of Hyperbolic Functions (6.7.3)
- Acceleration and the Derivative (7.1.1)
- Solving Word Problems Involving Distance and Velocity (7.1.2)
- High-Order Derivatives and Linear Approximation (7.2.1)
- Using the Tangent Line Approximation Formula (7.2.2)
- Newton's Method (7.2.3)
- The Connection between Slope and Optimization (7.3.1)
- The Fence Problem (7.3.2)
- The Box Problem (7.3.3)
- The Can Problem (7.3.4)
- The Wire-Cutting Problem (7.3.5)
- The Pebble Problem (7.4.1)
- The Ladder Problem (7.4.2)
- The Baseball Problem (7.4.3)
- The Blimp Problem (7.4.4)
- Math Anxiety (7.4.5)
- An Introduction to Curve Sketching (8.1.1)
- Three Big Theorems (8.1.2)
- Morale Moment (8.1.3)
- Critical Points (8.2.1)
- Maximum and Minimum (8.2.2)
- Regions Where a Function Increases or Decreases (8.2.3)
- The First Derivative Test (8.2.4)
- Math Magic (8.2.5)
- Concavity and Inflection Points (8.3.1)
- Using the Second Derivative to Examine Concavity (8.3.2)
- The Möbius Band (8.3.4)
- Graphs of Polynomial Functions (8.4.1)
- Cusp Points and the Derivative (8.4.2)
- Domain-Restricted Functions and the Derivative (8.4.3)
- The Second Derivative Test (8.4.4)
- Vertical Asymptotes (8.5.1)
- Horizontal Asymptotes and Infinite Limits (8.5.2)
- Graphing Functions with Asymptotes (8.5.3)
- Functions with Asymptotes and Holes (8.5.4)
- Functions with Asymptotes and Critical Points (8.5.5)
- Antidifferentiation (9.1.1)
- Antiderivatives of Powers of x (9.1.2)
- Antiderivatives of Trigonometric and Exponential Functions (9.1.3)
- Undoing the Chain Rule (9.2.1)
- Integrating Polynomials by Substitution (9.2.2)
- Integrating Composite Trigonometric Functions by Substitution (9.3.1)
- Integrating Composite Exponential and Rational Functions by Substitution (9.3.2)
- More Integrating Trigonometric Functions by Substitution (9.3.3)
- Choosing Effective Function Decompositions (9.3.4)
- Approximating Areas of Plane Regions (9.4.1)
- Areas, Riemann Sums, and Definite Integrals (9.4.2)
- The Fundamental Theorem of Calculus, Part 1 (9.4.3)
- The Fundamental Theorem of Calculus, Part II (9.4.4)
- Illustrating the Fundamental Theorem of Calculus (9.4.5)
- Evaluating Definite Integrals (9.4.6)
- An Overview of Trigonometric Substitution Strategy (9.5.1)
- Trigonometric Substitution Involving a Definite Integral: Part One (9.5.2)
- Trigonometric Substitution Involving a Definite Integral: Part Two (9.5.3)
- Deriving the Trapezoidal Rule (9.6.1)
- An Example of the Trapezoidal Rule (9.6.2)
- Antiderivatives and Motion (10.1.1)
- Gravity and Vertical Motion (10.1.2)
- Solving Vertical Motion Problems (10.1.3)
- The Area between Two Curves (10.2.1)
- Limits of Area and Integration (10.2.2)
- Common Mistakes to Avoid When Finding Areas (10.2.3)
- Regions Bound by Several Curves (10.2.4)
- Finding Areas by Integrating with Respect to y: Part One (10.3.1)
- Finding Areas by Integrating with Respect to y: Part Two (10.3.2)
- Area, Integration by Substitution, and Trigonometry (10.3.3)
- Finding the Average Value of a Function (10.4.1)
- Finding Volumes Using Cross-Sectional Slices (10.5.1)
- An Example of Finding Cross-Sectional Volumes (10.5.2)
- Solids of Revolution (10.6.1)
- The Disk Method along the y-Axis (10.6.2)
- A Transcendental Example of the Disk Method (10.6.3)
- The Washer Method across the x-Axis (10.6.4)
- The Washer Method across the y-Axis (10.6.5)
- Introducing the Shell Method (10.7.1)
- Why Shells Can Be Better Than Washers (10.7.2)
- The Shell Method: Integrating with Respect to y (10.7.3)
- An Introduction to Work (10.8.1)
- Calculating Work (10.8.2)
- Hooke's Law (10.8.3)
- Center of Mass (10.9.1)
- The Center of Mass of a Thin Plate (10.9.2)
- An Introduction to Arc Length (10.10.1)
- Finding Arc Lengths of Curves Given by Functions (10.10.2)
- An Introduction to Differential Equations (11.1.1)
- Solving Separable Differential Equations (11.1.2)
- Finding a Particular Solution (11.1.3)
- Direction Fields (11.1.4)
- Euler's Method for Solving Differential Equations Numerically (11.1.5)
- Exponential Growth (11.2.1)
- Logistic Growth (11.2.2)
- Radioactive Decay (11.2.3)
- Indeterminate Forms (12.1.1)
- An Introduction to L'Hôpital's Rule (12.1.2)
- Basic Uses of L'Hôpital's Rule (12.1.3)
- More Exotic Examples of Indeterminate Forms (12.1.4)
- L'Hôpital's Rule and Indeterminate Products (12.2.1)
- L'Hôpital's Rule and Indeterminate Differences (12.2.2)
- L'Hôpital's Rule and One to the Infinite Power (12.2.3)
- Another Example of One to the Infinite Power (12.2.4)
- The First Type of Improper Integral (12.3.1)
- The Second Type of Improper Integral (12.3.2)
- Infinite Limits of Integration, Convergence, and Divergence (12.3.3)
- An Introduction to Paradoxes (13.1.1)
- Paradoxes and Air Safety (13.1.2)
- A Glimpse Into Calculus II (13.3.1)
