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AP Calculus AB

This class was created by Brainscape user Anton Soloshenko. Visit their profile to learn more about the creator.

By: Anton Soloshenko
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Decks in this class (169)

An Introduction to Thinkwell Calculus (1.1.1)
Thinkwell calculus is designed to...,
The lecture environment is partit...
2  cards
The Two Questions of Calculus (1.1.2)
Use calculus to find instantaneou...,
Average rate of change r d t
2  cards
Average Rates of Change (1.1.3)
A change in one variable is often...,
Since division by 0 is undefined ...
2  cards
How to Do Math (1.1.4)
Practicing math problems is the b...
1  cards
Functions (1.2.1)
A function pairs one object with ...,
A function can be represented by ...,
You can evaluate a function for a...
3  cards
Graphing Lines (1.2.2)
A graph is a way of illustrating ...,
The slope intercept form y mx b a...,
When writing the equation of a li...
3  cards
Parabolas (1.2.3)
The graph of a second degree poly...,
When graphing functions start by ...,
The distance formula is an applic...
3  cards
Some Non-Euclidean Geometry (1.2.4)
No notes
1  cards
Finding Rate of Change over an Interval (2.1.1)
The position function relates tim...,
When solving a difficult problem ...
2  cards
Finding Limits Graphically (2.1.2)
In algebra you consider how a fun...,
The limit is the range value that...
2  cards
The Formal Definition of a Limit (2.1.3)
The concept of a limit can be exp...,
Formal definition of a limit let ...
2  cards
The Limit Laws, Part I (2.1.4)
Since limits are just numbers a l...
1  cards
The Limit Laws, Part II (2.1.5)
It is sometimes useful to examine...,
A limit exists only if the left h...
2  cards
One-Sided Limits (2.1.6)
Use the definition of the limit o...,
Understand and apply the limit la...,
Understand and apply limit laws f...
3  cards
The Squeeze Theorem (2.1.7)
Approximate the limit of a functi...,
Visualize the squeeze theorem gra...,
Find the exact limit of a functio...
3  cards
Continuity and Discontinuity (2.1.8)
A function is continuous at a poi...,
Three conditions must be met for ...
2  cards
Evaluating Limits (2.2.1)
The limit of a function is the ra...,
To evaluate a limit at a value wh...,
Limits that produce indeterminate...
3  cards
Limits and Intermediate Forms (2.2.2)
To evaluate a limit at a value wh...,
Limits that produce indeterminate...,
If direct substitution produces z...
3  cards
Two Techniques for Evaluating Limits (2.2.3)
When evaluating the limit of a co...,
An expression involving a binomia...
2  cards
On Overview of Limits (2.2.4)
The limit is the range value that...,
An indeterminate form is a mathem...
2  cards
Rates of Change, Secants, and Tangents (3.1.1)
Approximate the instantaneous rat...,
Represent the average rate of cha...,
Represent the instantaneous rate ...
4  cards
Finding Instantaneous Velocity (3.1.2)
The average rate of change is equ...,
By examining the average rate of ...,
To find the instantaneous rate ta...
4  cards
The Derivative (3.1.3)
What are tangent lines graphic re...,
How do you find the slope of a ta...,
What is the derivative function
3  cards
Differentiability (3.1.4)
Why may the derivative of a funct...,
If a function is differentiable t...
2  cards
The Slope of a Tangent Line (3.2.1)
How do you find the slope of a ta...,
The derivative of f at x is given...
2  cards
Instantaneous Rate (3.2.2)
How do you find the velocity of a...,
The derivative of f at x is given...
2  cards
The Equation of a Tangent Line (3.2.3)
To find the equation of a line ta...,
To find where the line tangent to...
2  cards
More on Instantaneous Rate (3.2.4)
How do you find the time when an ...,
How do you find the time when an ...
2  cards
The Derivative of the Reciprocal Function (3.3.1)
The derivative of f x x 1 is f x x 2,
To find the equation of a line ta...
2  cards
The Derivative of the Square Root Function (3.3.2)
The derivative of f x sqrt x is f...,
To find the instantaneous rate of...,
To find the time when an object i...
3  cards
A Shortcut for Finding Derivatives (4.1.1)
What is the shortcut that the pow...,
What does the power rule state
2  cards
A Quick Proof of the Power Rule (4.1.2)
In math it is not enough to find ...,
The power rule states that if n i...
2  cards
Uses of the Power Rule (4.1.3)
The power rule states that if n i...,
Given a differentiable function f...,
Given two differentiable function...
3  cards
The Product Rule (4.2.1)
The derivative of a product of tw...,
What does the product rule state
2  cards
The Quotient Rule (4.2.2)
Similar to the product rule the d...,
What does the quotient rule state
2  cards
An Introduction to the Chain Rule (4.3.1)
A composite function is made up o...,
The chain rule states that if f x...
2  cards
Using the Chain Rule (4.3.2)
The chain rule states that if f x...,
Some functions are actually combi...
2  cards
Combining Computational Techniques (4.3.3)
What does the chain rule state,
Why must multiple computational t...
2  cards
A Review of Trigonometry (5.1.1)
What does the pythagorean theorem...,
What is the pythagorean identity
2  cards
Graphic Trigonometric Functions (5.1.2)
What can angles be measured in an...,
How do you convert from radians t...,
The graphs of the trigonometric f...
3  cards
The Derivatives of Trigonometric Functions (5.1.3)
F x sin x f x cos x if f x cos x f x,
Use the derivatives of sine and c...
2  cards
The Number Pi (5.1.4)
Pi can be defined as the circumfe...,
The area of a circle can be appro...,
Trigonometric functions often inv...
3  cards
Graphing Exponential Functions (5.2.1)
An exponential function has the v...,
An exponential function cannot ha...
2  cards
Derivatives of Exponential Functions (5.2.2)
Studying the slopes of tangent li...,
How do you find the derivative of...
2  cards
Evaluating Logarithmic Functions (5.3.1)
Remember the change of base theor...,
A logarithm indicates the exponen...,
Logs to the base 10 are written w...
3  cards
The Derivative of the Natural Log Function (5.3.2)
The derivative of the natural exp...,
The natural exponential function ...
2  cards
Using the Derivative Rules with Transcendental Functions (5.3.3)
Some functions are combinations o...,
What are the derivatives of the t...
2  cards
An Introduction to Implicit Differentiation (6.1.1)
The definition of the derivative ...,
Leibniz notation is another way o...
2  cards
Finding the Derivative Implicitly (6.1.2)
Leibniz notation is another way o...,
Implicit differentiation uses the...
2  cards
Using Implicit Differentiation (6.2.1)
Find the derivative of a relation...
1  cards
Applying Implicit Differentiation (6.2.2)
What is implicit differentiation,
How do you find the equation of a...
2  cards
The Exponential and Natural Log Functions (6.3.1)
What is the exponential function,
What is the natural log function,
The exponential and natural log f...
3  cards
Differentiating Logarithmic Functions (6.3.2)
Find the derivative of a general ...,
Differentiate composite functions...,
Differentiate other complicated f...
3  cards
Logarithmic Differentiation (6.3.3)
Understand that the power rule of...,
Take the natural log of both side...,
Apply logarithmic differentiation...
3  cards
The Basics of Inverse Functions (6.3.4)
What do inverse functions do to e...,
What two things switch roles in a...,
Functions that are not one to one...
3  cards
Finding the Inverse of a Function (6.3.5)
To determine the inverse of a fun...,
Verify the inverse by composing i...
2  cards
Derivatives of Inverse Functions (6.4.1)
You can calculate the derivative ...
1  cards
The Inverse Sine, Cosine, and Tangent Functions (6.5.1)
What is the only way that allows ...,
How can you dictate inverse trigo...
2  cards
The Inverse Secant, Cosecant, and Cotangent Functions (6.5.2)
The standard trigonometric functi...
1  cards
Evaluating Inverse Trigonometric Functions (6.5.3)
To evaluate inverse trigonometric...,
An inverse trig function will not...
2  cards
Derivatives of Inverse Trigonometric Functions (6.6.1)
How do you find the derivative of...
1  cards
Defining the Hyperbolic Functions (6.7.1)
Hanging cables are called catenar...,
There are six hyperbolic function...
2  cards
Hyperbolic Identities (6.7.2)
When verifying a hyperbolic ident...,
The hyperbolic identities mirror ...,
The hyperbolic functions are deri...
3  cards
Derivatives of Hyperbolic Functions (6.7.3)
How do you differentiate hyperbol...,
What do the derivatives of the hy...
2  cards
Acceleration and the Derivative (7.1.1)
Velocity is the rate of change of...,
Tangent lines can be used to appr...
2  cards
Solving Word Problems Involving Distance and Velocity (7.1.2)
By collecting and analyzing physi...,
For an object to attain a maximum...,
Acceleration measures the rate of...
3  cards
High-Order Derivatives and Linear Approximation (7.2.1)
You can find successive derivativ...,
Derivatives can allow you to find...
2  cards
Using the Tangent Line Approximation Formula (7.2.2)
What is the tangent line approxim...
1  cards
Newton's Method (7.2.3)
Newton s method iterates the appr...
1  cards
The Connection between Slope and Optimization (7.3.1)
On an interval the sign of the de...,
Values that make the derivative o...
2  cards
The Fence Problem (7.3.2)
Values that make the derivative o...,
The fence problem involves maximi...
2  cards
The Box Problem (7.3.3)
What is the box problem
1  cards
The Can Problem (7.3.4)
Values that make the derivative o...,
The can problem involves maximizi...
2  cards
The Wire-Cutting Problem (7.3.5)
Values that make the derivative o...,
What is the wire cutting problem,
For a given perimeter a circle en...
3  cards
The Pebble Problem (7.4.1)
Related rate problems involve usi...,
The three steps to problem solvin...
2  cards
The Ladder Problem (7.4.2)
Related rate problems involve usi...,
Use implicit differentiation when...
2  cards
The Baseball Problem (7.4.3)
Related rate problems involve usi...,
Use implicit differentiation when...,
A negative value for the derivati...
3  cards
The Blimp Problem (7.4.4)
Related rate problems involve usi...,
Use implicit differentiation when...
2  cards
Math Anxiety (7.4.5)
No notes
1  cards
An Introduction to Curve Sketching (8.1.1)
Applications of the derivative in...,
The techniques used in algebra fo...
2  cards
Three Big Theorems (8.1.2)
The intermediate value theorem if...,
Rolle s theorem if f is continuou...,
The mean value theorem if f is co...
3  cards
Morale Moment (8.1.3)
No notes
1  cards
Critical Points (8.2.1)
What is a critical point,
How do you find critical points
2  cards
Maximum and Minimum (8.2.2)
Identify relative or local maxima...,
Understand the extreme value theo...,
Apply the closed interval method ...
3  cards
Regions Where a Function Increases or Decreases (8.2.3)
Critical points divide the curve ...,
On an interval the sign of the fi...
2  cards
The First Derivative Test (8.2.4)
Determining the sign of the deriv...,
The first derivative test states ...,
On an interval the sign of the fi...
3  cards
Math Magic (8.2.5)
No notes
1  cards
Concavity and Inflection Points (8.3.1)
The concavity of a graph can be d...,
If the second derivative of a fun...,
Points where the graph changes co...
3  cards
Using the Second Derivative to Examine Concavity (8.3.2)
The second derivative can be used...,
Knowing the critical points local...
2  cards
The Möbius Band (8.3.4)
No notes
1  cards
Graphs of Polynomial Functions (8.4.1)
To graph a function 1 find critic...,
On an interval the sign of the fi...
2  cards
Cusp Points and the Derivative (8.4.2)
Functions with fractional exponen...,
To graph a function 1 find critic...
2  cards
Domain-Restricted Functions and the Derivative (8.4.3)
If the variable of a function is ...,
To graph a function 1 find critic...,
On an interval the sign of the fi...
3  cards
The Second Derivative Test (8.4.4)
If the graph of a function has a ...,
If the graph of a function has a ...,
The second derivative test states...
3  cards
Vertical Asymptotes (8.5.1)
What are asymptotes,
How do you identify vertical asym...,
How can you tell if there may be ...
3  cards
Horizontal Asymptotes and Infinite Limits (8.5.2)
What are asymptotes,
How do you identify horizontal as...,
Examine the highest powered term ...
3  cards
Graphing Functions with Asymptotes (8.5.3)
Identify vertical asymptotes for ...,
Identify horizontal asymptotes by...,
The behavior of a function can ch...
3  cards
Functions with Asymptotes and Holes (8.5.4)
Identify vertical asymptotes for ...,
Identify horizontal asymptotes by...,
A hole or point discontinuity occ...
3  cards
Functions with Asymptotes and Critical Points (8.5.5)
Identify vertical asymptotes for ...,
Identify horizontal asymptotes by...,
The behavior of a function can ch...
3  cards
Antidifferentiation (9.1.1)
If you want to undo the derivativ...,
Antidifferentiation is a process ...,
Given two functions f and f f is ...
3  cards
Antiderivatives of Powers of x (9.1.2)
Given two functions f and f f is ...,
If a function has an antiderivati...,
The properties of antidifferentia...
3  cards
Antiderivatives of Trigonometric and Exponential Functions (9.1.3)
Given two functions f and f f is ...,
Discover integration formulas by ...
2  cards
Undoing the Chain Rule (9.2.1)
Since differentiation and integra...,
One method for evaluating integra...
2  cards
Integrating Polynomials by Substitution (9.2.2)
The differential of an integral i...,
Integration by substitution is a ...
2  cards
Integrating Composite Trigonometric Functions by Substitution (9.3.1)
Integration by substitution is a ...,
If the du expression is only off ...
2  cards
Integrating Composite Exponential and Rational Functions by Substitution (9.3.2)
Integration by substitution is a ...,
You may need to experiment with s...
2  cards
More Integrating Trigonometric Functions by Substitution (9.3.3)
You can apply integration by subs...,
When working with integrands that...
2  cards
Choosing Effective Function Decompositions (9.3.4)
Experiment with different choices...,
When working with integrands that...
2  cards
Approximating Areas of Plane Regions (9.4.1)
The two key questions of calculus...,
When trying to find the area of a...
2  cards
Areas, Riemann Sums, and Definite Integrals (9.4.2)
As the number of rectangles used ...,
A function and the equation for t...,
The definite integral of f from a...
3  cards
The Fundamental Theorem of Calculus, Part 1 (9.4.3)
Understand the fundamental theore...,
Apply the fundamental theorem of ...
2  cards
The Fundamental Theorem of Calculus, Part II (9.4.4)
Let f be defined on the interval ...,
The fundamental theorem of calcul...,
The fundamental theorem of calcul...
3  cards
Illustrating the Fundamental Theorem of Calculus (9.4.5)
The fundamental theorem of calcul...,
When the limits of integration ar...,
The fundamental theorem of calcul...
3  cards
Evaluating Definite Integrals (9.4.6)
When working with integration by ...,
Since there is a connection betwe...,
Another way to evaluate definite ...
3  cards
An Overview of Trigonometric Substitution Strategy (9.5.1)
Use trigonometric substitution to...
1  cards
Trigonometric Substitution Involving a Definite Integral: Part One (9.5.2)
Use trigonometric substitution to...
1  cards
Trigonometric Substitution Involving a Definite Integral: Part Two (9.5.3)
How do you solve a definite integ...,
What purpose does the labeled rig...
2  cards
Deriving the Trapezoidal Rule (9.6.1)
The trapezoidal rule approximates...
1  cards
An Example of the Trapezoidal Rule (9.6.2)
The trapezoidal rule approximates...
1  cards
Antiderivatives and Motion (10.1.1)
Position and motion can be analyz...,
Velocity is the rate of change of...,
Given the velocity function of an...
5  cards
Gravity and Vertical Motion (10.1.2)
The acceleration due to gravity o...,
Given the initial velocity and in...,
The velocity and position functio...
3  cards
Solving Vertical Motion Problems (10.1.3)
Given the initial velocity and in...,
The velocity and position functio...
2  cards
The Area between Two Curves (10.2.1)
The definite integral can be used...,
To find the area of a region boun...
2  cards
Limits of Area and Integration (10.2.2)
To find the area of a region boun...
1  cards
Common Mistakes to Avoid When Finding Areas (10.2.3)
When evaluating areas of regions ...,
When finding the area between the...
2  cards
Regions Bound by Several Curves (10.2.4)
Sometimes regions can be defined ...
1  cards
Finding Areas by Integrating with Respect to y: Part One (10.3.1)
Sometimes it is easier to stack h...,
Area between two curves lim b a f...
2  cards
Finding Areas by Integrating with Respect to y: Part Two (10.3.2)
Area between two curves defined i...,
When finding the area of a region...
2  cards
Area, Integration by Substitution, and Trigonometry (10.3.3)
Area between two curves defined i...,
When finding the area of a region...
2  cards
Finding the Average Value of a Function (10.4.1)
The average value of a function o...,
Average value 1 b a lim b a f x dx
2  cards
Finding Volumes Using Cross-Sectional Slices (10.5.1)
The volume of a solid with vertic...,
The volume of a solid with horizo...
2  cards
An Example of Finding Cross-Sectional Volumes (10.5.2)
The volume of a solid with vertic...,
The volume of a solid with horizo...
2  cards
Solids of Revolution (10.6.1)
Revolving a plane region about a ...,
Using the disk method the volume ...
2  cards
The Disk Method along the y-Axis (10.6.2)
Revolving a plane region about a ...,
Using the disk method the volume ...
2  cards
A Transcendental Example of the Disk Method (10.6.3)
Revolving a plane region about a ...,
Using the disk method the volume ...
2  cards
The Washer Method across the x-Axis (10.6.4)
Using the disk method the volume ...,
Washers are disks with smaller di...
2  cards
The Washer Method across the y-Axis (10.6.5)
Using the disk method the volume ...,
Washers are disks with smaller di...
2  cards
Introducing the Shell Method (10.7.1)
Using the shell method the volume...
1  cards
Why Shells Can Be Better Than Washers (10.7.2)
Using the shell method the volume...,
For some solids the shell method ...
2  cards
The Shell Method: Integrating with Respect to y (10.7.3)
Using the shell method the volume...
1  cards
An Introduction to Work (10.8.1)
Work is the energy used when appl...,
For a constant force f work is th...,
For a changing or variable force ...
3  cards
Calculating Work (10.8.2)
Work is the energy used when appl...,
For a changing or variable force ...
2  cards
Hooke's Law (10.8.3)
Work is the energy used when appl...,
Use hooke s law to determine how ...
2  cards
Center of Mass (10.9.1)
The center of mass of an object i...,
A moment can be thought of as a s...,
The center of mass x y can be fou...
3  cards
The Center of Mass of a Thin Plate (10.9.2)
The center of mass of an object i...,
The center of mass of a thin plat...
2  cards
An Introduction to Arc Length (10.10.1)
Arc length is the length of the c...,
The arc length of a smooth curve ...
2  cards
Finding Arc Lengths of Curves Given by Functions (10.10.2)
The arc length of a smooth curve ...
1  cards
An Introduction to Differential Equations (11.1.1)
A differential equation is an equ...,
Not all differential equations ca...
2  cards
Solving Separable Differential Equations (11.1.2)
To solve a separable differential...,
Initial conditions allow you to f...
2  cards
Finding a Particular Solution (11.1.3)
Given a point you can use the gen...
1  cards
Direction Fields (11.1.4)
Given a first order differential ...,
The direction field illustrates t...
2  cards
Euler's Method for Solving Differential Equations Numerically (11.1.5)
Compute and graph approximate sol...,
When the exact solution is known ...
2  cards
Exponential Growth (11.2.1)
Population growth can be modeled ...
1  cards
Logistic Growth (11.2.2)
Distinguish between exponential g...,
Analyze solutions to logistic gro...,
Solve logistic growth equations n...
4  cards
Radioactive Decay (11.2.3)
Radioactive substances decay over...,
The same equations that govern ex...
2  cards
Indeterminate Forms (12.1.1)
A limit of a function is called a...,
Some indeterminate forms can be s...
2  cards
An Introduction to L'Hôpital's Rule (12.1.2)
A limit of a function is called a...,
Lhopitals rule enables you to eva...
2  cards
Basic Uses of L'Hôpital's Rule (12.1.3)
When evaluating a limit it is alw...,
As long as the limit is still an ...,
L hopital s rule might not produc...
3  cards
More Exotic Examples of Indeterminate Forms (12.1.4)
As long as the limit still produc...,
When applying l hopital s rule to...,
L hopital s rule might not give y...
3  cards
L'Hôpital's Rule and Indeterminate Products (12.2.1)
Some indeterminate forms have to ...,
When applying l hopital s rule to...
2  cards
L'Hôpital's Rule and Indeterminate Differences (12.2.2)
Some indeterminate forms have to ...,
Look for a common denominator or ...
2  cards
L'Hôpital's Rule and One to the Infinite Power (12.2.3)
Some indeterminate forms have to ...,
In order to apply l hopital s rul...
2  cards
Another Example of One to the Infinite Power (12.2.4)
Some indeterminate forms have to ...,
In order to apply l hopital s rul...
2  cards
The First Type of Improper Integral (12.3.1)
An improper integral is a definit...,
With some improper integrals the ...,
An improper integral that is infi...
3  cards
The Second Type of Improper Integral (12.3.2)
If a function is not continuous o...
1  cards
Infinite Limits of Integration, Convergence, and Divergence (12.3.3)
Improper integrals can be express...
1  cards
An Introduction to Paradoxes (13.1.1)
No notes
1  cards
Paradoxes and Air Safety (13.1.2)
No notes
1  cards
A Glimpse Into Calculus II (13.3.1)
Calculus ii explores new techniqu...,
Calculus ii delves deeper into th...
2  cards

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