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AP®︎ Toán cao cấp BC
Defining limits and using limit notation: Limits and continuityƯớc lượng giới hạn hàm số khi biết đồ thị: Limits and continuityDetermining limits using algebraic properties of limits: limit properties: Limits and continuityDetermining limits using algebraic properties of limits: direct substitution: Limits and continuityDetermining limits using algebraic manipulation: Limits and continuitySelecting procedures for determining limits: Limits and continuity
Determining limits using the squeeze theorem: Limits and continuityExploring types of discontinuities: Limits and continuityDefining continuity at a point: Limits and continuityConfirming continuity over an interval: Limits and continuityRemoving discontinuities: Limits and continuityConnecting infinite limits and vertical asymptotes: Limits and continuityConnecting limits at infinity and horizontal asymptotes: Limits and continuity
Defining average and instantaneous rates of change at a point: Differentiation: definition and basic derivative rulesDefining the derivative of a function and using derivative notation: Differentiation: definition and basic derivative rulesConnecting differentiability and continuity: determining when derivatives do and do not exist: Differentiation: definition and basic derivative rulesApplying the power rule: Differentiation: definition and basic derivative rulesDerivative rules: constant, sum, difference, and constant multiple: introduction: Differentiation: definition and basic derivative rules
Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule: Differentiation: definition and basic derivative rulesDerivatives of cos(x), sin(x), 𝑒ˣ, and ln(x): Differentiation: definition and basic derivative rulesThe product rule: Differentiation: definition and basic derivative rulesThe quotient rule: Differentiation: definition and basic derivative rulesFinding the derivatives of tangent, cotangent, secant, and/or cosecant functions: Differentiation: definition and basic derivative rulesOptional videos: Differentiation: definition and basic derivative rules
Extreme value theorem, global versus local extrema, and critical points: Applying derivatives to analyze functions Determining intervals on which a function is increasing or decreasing: Applying derivatives to analyze functions Using the first derivative test to find relative (local) extrema: Applying derivatives to analyze functions Using the candidates test to find absolute (global) extrema: Applying derivatives to analyze functions
Determining concavity of intervals and finding points of inflection: graphical: Applying derivatives to analyze functions Using the second derivative test to find extrema: Applying derivatives to analyze functions Sketching curves of functions and their derivatives: Applying derivatives to analyze functions Connecting a function, its first derivative, and its second derivative: Applying derivatives to analyze functions Solving optimization problems: Applying derivatives to analyze functions
Exploring accumulations of change: Integration and accumulation of changeRiemann sums, summation notation, and definite integral notation: Integration and accumulation of changeApplying properties of definite integrals: Integration and accumulation of changeĐịnh nghĩa tích phân: Integration and accumulation of changeFinding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule: Integration and accumulation of changeFinding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals: Integration and accumulation of change
Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals: Integration and accumulation of changeIntegrating using substitution: Integration and accumulation of changeIntegrating functions using long division and completing the square: Integration and accumulation of changeUsing integration by parts: Integration and accumulation of changeIntegrating using linear partial fractions: Integration and accumulation of changeEvaluating improper integrals: Integration and accumulation of change
Finding arc lengths of curves given by parametric equations: Parametric equations, polar coordinates, and vector-valued functionsSolving motion problems using parametric and vector-valued functions: Parametric equations, polar coordinates, and vector-valued functionsFinding the area of a polar region or the area bounded by a single polar curve: Parametric equations, polar coordinates, and vector-valued functions
Defining convergent and divergent infinite series: Infinite sequences and seriesWorking with geometric series: Infinite sequences and seriesThe nth-term test for divergence: Infinite sequences and seriesIntegral test for convergence: Infinite sequences and seriesHarmonic series and p-series: Infinite sequences and seriesComparison tests for convergence: Infinite sequences and seriesAlternating series test for convergence: Infinite sequences and seriesRatio test for convergence: Infinite sequences and series
Determining absolute or conditional convergence: Infinite sequences and seriesAlternating series error bound: Infinite sequences and seriesFinding Taylor polynomial approximations of functions: Infinite sequences and seriesLagrange error bound: Infinite sequences and seriesRadius and interval of convergence of power series: Infinite sequences and seriesFinding Taylor or Maclaurin series for a function: Infinite sequences and seriesRepresenting functions as power series: Infinite sequences and seriesOptional videos: Infinite sequences and series