Calculus AB / BC Study Library.

Average and instantaneous rates of change · Limit evaluation: algebraic, graphical, and tabular approaches · Squeeze Theorem · Continuity at a point and on an interval · Intermediate Value Theorem (IVT) · Infinite limits and vertical asymptotes · Limits at infinity and horizontal asymptotes · Removable and non-removable discontinuities

Limit definition of the derivative · Differentiability and its relationship to continuity · Power rule · Sum, difference, and constant multiple rules · Derivatives of trigonometric functions (sin, cos, tan, csc, sec, cot) · Derivatives of exponential functions (e^x, a^x) · Derivatives of natural logarithm and general logarithms · Product rule · Quotient rule

Chain rule for composite functions · Implicit differentiation · Derivatives of inverse functions · Derivatives of inverse trigonometric functions (arcsin, arccos, arctan) · Higher-order derivatives (second, third, nth derivative)

Interpretation of the derivative as an instantaneous rate of change · Related rates problems · Linear approximation using the tangent line (local linearization) · L'Hôpital's Rule for indeterminate forms (0/0, ∞/∞) · Motion problems: position, velocity, acceleration, and speed · Interpreting the sign of velocity and acceleration

Mean Value Theorem (MVT) · Extreme Value Theorem (EVT) · Critical points and local extrema · First derivative test for local maxima and minima · Second derivative test for local maxima and minima · Concavity and inflection points · Global (absolute) extrema on closed intervals · Optimization problems · Curve sketching using derivatives

Riemann sums (LRAM, RRAM, Midpoint, Trapezoidal) · Definite integrals as limits of Riemann sums · Fundamental Theorem of Calculus Part 1 · Fundamental Theorem of Calculus Part 2 · u-substitution for indefinite and definite integrals · Accumulation functions and their derivatives · Properties of definite integrals

Slope fields: constructing and interpreting · Matching slope fields to differential equations · Separable differential equations · Solving initial value problems (IVPs) · Exponential growth and decay models · General and particular solutions

Average value of a function on an interval · Area between curves · Volumes of solids with known cross-sections · Volumes of solids of revolution: disk method · Volumes of solids of revolution: washer method · Position, velocity, and displacement using integration · Total distance traveled vs. net displacement

Derivatives of parametric equations: dy/dx and d²y/dx² · Arc length of a parametric curve · Vector-valued functions: position, velocity, and acceleration vectors · Motion along a curve in the plane using vectors · Speed as the magnitude of the velocity vector · Polar coordinates and the relationship to rectangular coordinates · Area enclosed by a polar curve · Arc length of a polar curve

Convergence and divergence of sequences · Geometric series: convergence condition and sum formula · p-series: convergence condition · nth-term divergence test · Integral test for convergence · Comparison test and limit comparison test · Ratio test · Alternating series test (AST) and alternating series error bound · Power series and radius/interval of convergence · Taylor series and Maclaurin series · Maclaurin series for e^x, sin x, cos x, 1/(1-x), and ln(1+x) · Lagrange error bound for Taylor polynomial approximations