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Contextual applications of differentiation

AP Calc: CHA (BI), CHA‑3 (EU), LIM (BI), LIM‑4 (EU)
AP Calc: CHA (BI), CHA‑3 (EU), CHA‑3.A (LO), CHA‑3.A.1 (EK), CHA‑3.A.2 (EK), CHA‑3.A.3 (EK)
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Interpreting the meaning of the derivative in contextAnalyzing problems involving rates of change in applied contexts
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AP Calc: CHA (BI), CHA‑3 (EU), CHA‑3.B (LO), CHA‑3.B.1 (EK)
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Introduction to one-dimensional motion with calculusInterpreting direction of motion from position-time graphInterpreting direction of motion from velocity-time graphInterpreting change in speed from velocity-time graphWorked example: Motion problems with derivatives
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Interpret motion graphsGet 3 of 4 questions to level up!
Motion problems (differential calc)Get 3 of 4 questions to level up!
AP Calc: CHA (BI), CHA‑3 (EU), CHA‑3.C (LO), CHA‑3.C.1 (EK)
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Applied rate of change: forgetfulness
AP Calc: CHA (BI), CHA‑3 (EU), CHA‑3.D (LO), CHA‑3.D.1 (EK), CHA‑3.D.2 (EK)
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Related rates introAnalyzing problems involving related ratesAnalyzing related rates problems: expressionsAnalyzing related rates problems: equations (Pythagoras)Analyzing related rates problems: equations (trig)Differentiating related functions introWorked example: Differentiating related functions
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Differentiate related functionsGet 3 of 4 questions to level up!
AP Calc: CHA (BI), CHA‑3 (EU), CHA‑3.E (LO), CHA‑3.E.1 (EK)
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Related rates: Approaching carsRelated rates: Falling ladderRelated rates: water pouring into a coneRelated rates: shadowRelated rates: balloon
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Related rates introGet 3 of 4 questions to level up!
Related rates (multiple rates)Get 3 of 4 questions to level up!
Related rates (Pythagorean theorem)Get 3 of 4 questions to level up!
Related rates (advanced)Get 3 of 4 questions to level up!
AP Calc: CHA (BI), CHA‑3 (EU), CHA‑3.F (LO), CHA‑3.F.1 (EK)
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Local linearityLocal linearity and differentiabilityWorked example: Approximation with local linearityLinear approximation of a rational function
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Approximation with local linearityGet 3 of 4 questions to level up!
AP Calc: LIM (BI), LIM‑4 (EU), LIM‑4.A (LO), LIM‑4.A.1 (EK), LIM‑4.A.2 (EK)
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L'Hôpital's rule introductionL'Hôpital's rule: limit at 0 exampleL'Hôpital's rule: limit at infinity exampleProof of special case of l'Hôpital's rule
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L'Hôpital's rule: 0/0Get 3 of 4 questions to level up!
L'Hôpital's rule: ∞/∞Get 3 of 4 questions to level up!
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Proof of special case of l'Hôpital's rule

About this unit

Derivatives describe the rate of change of quantities. This becomes very useful when solving various problems that are related to rates of change in applied, real-world, situations. Also learn how to apply derivatives to approximate function values and find limits using L’Hôpital’s rule.
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