Best AP Calculus AB/BC Quizlet Decks By Unit

Best AP Calculus AB/BC Quizlet Decks By Unit

Unit 1: Limits and Continuity

Key Terms:

• Limit - The value that a function approaches as x gets infinitely close to a constant (notated as lim x→a f(x))
• Continuous - The graph is a smooth unbroken curve (The limit exists!)
• Removable Discontinuity - A hole in the graph, typically removed via factoring and canceling out

Unit 2: Differentiation: Definition and Fundamental Properties

Key Terms:

• Derivative (Limit Definition) - df/dx = lim h→0 [f(x+h) - f(x)]/h
• Tangent Line - A line that touches a function only once
• Basic Derivative Rules - Product rule, quotient rule, sum and difference rule

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

Key Terms:

• Derivative of a Composite Function - Chain rule - d/dx f(g(x)) = f’(g(x)) * g’(x)
• Derivative of Implicit Functions - Differentiate with respect to x and use the chain rule. Ex. In the equation x^2 + y^2 = 4, 2x + 2y dy/dx = 0.
• Derivative of Inverse Functions - d/dx (f^-1(x)) = 1/f’(f^-1(x))

Unit 4: Contextual Applications of Differentiation

Key Terms:

• Related Rates - A type of problem that requires you to use implicit differentiation to find a relationship between two rates
• Position, Velocity, and Acceleration - If position = s(t), velocity is v(t) = s’(t) and acceleration is a(t) = v’(t) = s’’(t).
• L’Hopitals Rule - If we have an indeterminate form 0/0 or ∞/∞ all we need to do is differentiate the numerator and differentiate the denominator and then take the limit

Unit 5: Analytical Applications of Differentiation

Key Terms:

• Absolute and Relative Extrema - The minimum and maximum points on a graph, absolute extrema require you to test endpoints and find the highest or lowest point on an interval, relative extrema require you to find where f’(x) switches sign
• Concavity - The rate at which the derivative is changing, notated by f’’(x). If f’’(x) < 0, it is concave down and vice versa.
• Mean Value Theorem - If f(x) is continuous on the interval [a, b] and differentiable on the interval (a, b), there is a point c ∈ [a, b] where f’(c) = f(b) - f(a)/b - a (there is a point where the derivative equals the average rate)

Unit 6: Integration and Accumulation of Change

Key Terms:

• Antiderivative: The opposite of a derivative. Ex. the antiderivative of 2x is x^2 + C. NEVER FORGET THE +C!!! Because constants become zero in a derivative, the +C accounts for it.
• Riemann Sum - A way of approximating an integral by using infinitesimally small rectangles
• Accumulation of Change - Integrals represent an accumulation of change over a given region and can be used to calculate aggregates and totals this way
• (BC Only) Integration by Parts - A way to integrate products with the formula: the integral of udv = uv - the integral of vdu
• (BC Only) Integration by Partial Fractions - A way to integrate complex fractions by splitting the fraction into smaller partial fractions and then integrating each term separately
• (BC Only) Improper Integrals - An integral containing a point in which the value of the function is undefined or contains x = positive or negative infinity

Unit 7: Differential Equations

Key Terms:

• Separable Diff. Eq - A differential equation in the form dy/dx = f(x)g(y)
• Exponential Growth - A situation in which a function is proportional to itself, represented by dy/dx = ky where k is a constant (The solution is in the form Ce^kx)
• (BC Only) Euler’s Method - A numerical method to approximate a particular solution by taking tiny steps from an initial condition
• (BC Only) Logistic Model - A differential equation in the form dy/dx=ky(L-y) where k is a constant and L is the carrying capacity. The solution is in the form L/(1+Ce^(-Lkt))

Unit 8: Applications of Integration

Key Terms:

• Solids of Revolution - A solid formed by revolving a function (or area between two functions) around either the x or y-axes
• Average Value Formula - On the interval [a, b], the average value of a function is 1/b-a * the integral from a to b of f(x) dx.
• Disk Method - Where you have one function bounded by an axis. V = pi * the integral from a to b of R(x)^2 dx.
• Washer Method - Used when your volume has a hole in it, or if you have a major and minor radius. V = pi * integral from a to b of (R(x)^2 - r(x)^2) dx.
• (BC Only) Arc length - Use to find the arc length of a function. S = integral from a to b of sqrt(1+(dy/dx)^2) dx

(BC Only) Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions

Key Terms:

• Polar Equation - A function in terms of the angle counterclockwise from the x-axis and the distance from the origin
• Parametric Equations - A function in which the x- and y-coordinates are in terms of a parameter t
• Vector-Valued Functions - Like parametric equations, but each point on the graph is represented by a vector from the origin

(BC Only) Unit 10: Infinite Sequences and Series

Key Terms:

• Convergence - When the value of an infinite series can be found
• Power series representation - An infinite series where the terms are of form a_nx^n where n is a non-negative integer
• Taylor Series - The power series representation of a function not centered at x=0
• MacLaurin Series - The power series representation of a function centered at x=0
• Alternating Series/Lagrange Error Bound - Although two separate concepts used in two very different situations, these are almost the same. The difference between the actual function and a partial sum approximation. No more than the value of the next term in the series