Κύριο περιεχόμενο
AP®︎ Λογισμός BC
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 rulesEstimating derivatives of a function at a point: 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
The chain rule: introduction: Differentiation: composite, implicit, and inverse functionsThe chain rule: further practice: Differentiation: composite, implicit, and inverse functionsΕμμεση διαφοροποίηση: Differentiation: composite, implicit, and inverse functionsDifferentiating inverse functions: Differentiation: composite, implicit, and inverse functionsDifferentiating inverse trigonometric functions: Differentiation: composite, implicit, and inverse functions
Selecting procedures for calculating derivatives: strategy: Differentiation: composite, implicit, and inverse functionsSelecting procedures for calculating derivatives: multiple rules: Differentiation: composite, implicit, and inverse functionsCalculating higher-order derivatives: Differentiation: composite, implicit, and inverse functionsFurther practice connecting derivatives and limits: Differentiation: composite, implicit, and inverse functionsOptional videos: Differentiation: composite, implicit, and inverse functions
Interpreting the meaning of the derivative in context: Contextual applications of differentiationStraight-line motion: connecting position, velocity, and acceleration: Contextual applications of differentiationRates of change in other applied contexts (non-motion problems): Contextual applications of differentiationIntroduction to related rates: Contextual applications of differentiation
Solving related rates problems: Contextual applications of differentiationApproximating values of a function using local linearity and linearization: Contextual applications of differentiationUsing L’Hôpital’s rule for finding limits of indeterminate forms: Contextual applications of differentiationOptional videos: Contextual applications of differentiation
Χρησιμοποιώντας το Θεώρημα Μέσης Τιμής: Applying derivatives to analyze functions 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
Determining concavity of intervals and finding points of inflection: algebraic: 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 behaviors of implicit relations: Applying derivatives to analyze functions Calculator active practice: Applying derivatives to analyze functions
Exploring accumulations of change: Integration and accumulation of changeApproximating areas with Riemann sums: Integration and accumulation of changeRiemann sums, summation notation, and definite integral notation: Integration and accumulation of changeThe fundamental theorem of calculus and accumulation functions: Integration and accumulation of changeInterpreting the behavior of accumulation functions involving area: Integration and accumulation of changeApplying properties of definite integrals: Integration and accumulation of changeThe fundamental theorem of calculus and definite integrals: Integration and accumulation of changeFinding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule: Integration and accumulation of change
Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals: Integration and accumulation of changeFinding 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 changeOptional videos: Integration and accumulation of change
Modeling situations with differential equations: Differential equationsVerifying solutions for differential equations: Differential equationsSketching slope fields: Differential equationsReasoning using slope fields: Differential equations
Approximating solutions using Euler’s method: Differential equationsFinding general solutions using separation of variables: Differential equationsFinding particular solutions using initial conditions and separation of variables: Differential equationsExponential models with differential equations: Differential equationsLogistic models with differential equations: Differential equations
Finding the average value of a function on an interval: Applications of integrationConnecting position, velocity, and acceleration functions using integrals: Applications of integrationUsing accumulation functions and definite integrals in applied contexts: Applications of integrationFinding the area between curves expressed as functions of x: Applications of integrationFinding the area between curves expressed as functions of y: Applications of integrationFinding the area between curves that intersect at more than two points: Applications of integrationVolumes with cross sections: squares and rectangles: Applications of integration
Όγκος με διατομές: τρίγωνα και ημικύκλια: Applications of integrationVolume with disc method: revolving around x- or y-axis: Applications of integrationVolume with disc method: revolving around other axes: Applications of integrationVolume with washer method: revolving around x- or y-axis: Applications of integrationVolume with washer method: revolving around other axes: Applications of integrationThe arc length of a smooth, planar curve and distance traveled: Applications of integrationCalculator active practice: Applications of integration
Defining and differentiating parametric equations: Parametric equations, polar coordinates, and vector-valued functionsSecond derivatives of parametric equations: Parametric equations, polar coordinates, and vector-valued functionsFinding arc lengths of curves given by parametric equations: Parametric equations, polar coordinates, and vector-valued functions
Defining and differentiating vector-valued functions: Parametric equations, polar coordinates, and vector-valued functionsSolving motion problems using parametric and vector-valued functions: Parametric equations, polar coordinates, and vector-valued functionsDefining polar coordinates and differentiating in polar form: 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