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AP®︎ Calculus BC (2017 edition)
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About the course: Limits and continuityAnalyzing limits graphically: Limits and continuityAnalyzing limits numerically: Limits and continuityOne-sided limits: Limits and continuityContinuity: Limits and continuityLimit rules for sums, differences, products, quotients, & composites: Limits and continuityDetermining limits using direct substitution: Limits and continuity
Determining limits by factoring & rationalizing: Limits and continuityTrigonometric limits & squeeze theorem: Limits and continuityInfinite limits intro: Limits and continuityAnalyzing limits at infinity: Limits and continuityAnalyzing functions for discontinuities: Limits and continuityStrategy in finding limits: Limits and continuityOptional videos: Limits and continuity
Basic differentiation rules: Derivative rulesPower rule: Derivative rulesPolynomial functions differentiation: Derivative rulesDerivatives of negative and fractional powers with power rule: Derivative rulesDerivatives of sin(x) and cos(x): Derivative rulesProduct rule: Derivative rules
Quotient rule: Derivative rulesRational functions differentiation: Derivative rulesChain rule: Derivative rulesRadical functions differentiation: Derivative rulesTrigonometric functions differentiation: Derivative rulesStrategy in differentiating functions: Derivative rulesOptional videos: Derivative rules
L'Hôpital's rule: Using derivatives to analyze functionsJustifying properties of functions using the first derivative: Using derivatives to analyze functionsCritical points & intervals of increase or decrease: Using derivatives to analyze functionsFinding relative extrema (first derivative test): Using derivatives to analyze functionsFinding absolute extrema: Using derivatives to analyze functions
Concavity & inflection points intro: Using derivatives to analyze functionsJustifying properties of functions using the second derivative: Using derivatives to analyze functionsFinding inflection points & analyzing concavity: Using derivatives to analyze functionsConnecting ƒ, ƒ’, and ƒ’’: Using derivatives to analyze functionsOptional videos: Using derivatives to analyze functions
Antiderivatives and indefinite integrals intro: Antiderivatives and the fundamental theorem of calculusFundamental theorem of calculus: Antiderivatives and the fundamental theorem of calculusIndefinite integrals: reverse power rule: Antiderivatives and the fundamental theorem of calculusIndefinite integrals of sin(x), cos(x), eˣ, and 1/x: Antiderivatives and the fundamental theorem of calculusFinding definite integrals: Antiderivatives and the fundamental theorem of calculusImproper integrals: Antiderivatives and the fundamental theorem of calculus
𝘶-substitution: Antiderivatives and the fundamental theorem of calculusIntegration by parts: Antiderivatives and the fundamental theorem of calculusPartial fraction expansion: Antiderivatives and the fundamental theorem of calculusAverage value of a function: Antiderivatives and the fundamental theorem of calculusInterpreting behavior of 𝑔 from graph of 𝑔'=ƒ: Antiderivatives and the fundamental theorem of calculusOptional videos: Antiderivatives and the fundamental theorem of calculus
Word problems involving definite integrals: Applications of definite integralsMotion problems (with integrals): Applications of definite integralsArea: vertical areas between curves: Applications of definite integralsArea: horizontal areas between curves: Applications of definite integralsArea: polar curves: Applications of definite integrals