Unit 4 Contextual Applicationsap Calculus

Unit 4 begins by developing understanding of average and instantaneous rates of change in problems involving motion. The unit then identifies differentiation as a common underlying structure on which to build understanding of change in a variety of contexts.

1. Unit 4 COntextual Applications Watch the video below while filling out Notes.
2. AP Calculus BC – Worksheet 29 Unit 4 Review: Contextual Applications of the Derivative 1 If f x x( ) 2 2 x, approximate f(3.1) using linearization centered at a 3. 2 3 The function 3 sin 0.01sin 4 0.02cos 40.7t t Q t e t t §¨¸ ©¹ models the electric charge, measured in coulombs, inside a lightbulb t seconds after it is turned on.
3. First Semester (Calculus AP) Syllabus A video tour of the curriculum Calculator doc/video listing Enrichment topics Rev 1 Adobe Flash Player is required to watch the videos.

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ENDURING UNDERSTANDING

CHA-3 Derivatives allow us to solve real-world problems involving rates of change.

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 Topic Name Essential Knowledge 4.1 Interpreting the Meaning of the Derivative in ContextLEARNING OBJECTIVECHA-3.A Interpret the meaning of a derivative in context. CHA-3.A.1 The derivative of a function can be interpreted as the instantaneous rate of change with respect to its independent variable. CHA-3.A.2 The derivative can be used to express information about rates of change in applied contexts. CHA-3.A.3 The unit for is the unit for f divided by the unit for x.

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At Just the Right Time A good problem

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 4.2 Straight Line Motion: Connecting Position, Velocity, and AccelerationLEARNING OBJECTIVECHA-3.B Calculate rates of change in applied contexts. CHA-3.B.1 The derivative can be used to solve rectilinear motion problems involving position, speed, velocity, and acceleration.

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The Ubiquitous Particle Motion Problem – a PowerPoint Presentation and its Handout

Motion Problems: Same Thing Different Context (11-16-2012) Matching Motion (9-16-2016)

Motion Matching A quick quiz

Speed (11-19-2012)

Speed Activity An exploration on Speed

A Note on Speed (4-21-2018) An analytic approach

Brian Leonard’s Particle Motion Game Velocity Game and answers Velocity game Answers

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 4.3 Rates of Change in Applied Contexts Other than MotionLEARNING OBJECTIVECHA-3.C Interpret rates of change in applied contexts. CHA-3.C.1 The derivative can be used to solve problems involving rates of change in applied contexts.

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 4.4 Introduction to Related RatesLEARNING OBJECTIVECHA-3.D Calculate related rates in applied contexts. CHA-3.D.1 The chain rule is the basis for differentiating variables in a related rates problem with respect to the same independent variable. CHA-3.D.2 Other differentiation rules, such as the product rule and the quotient rule, may also be necessary to differentiate all variables with respect to the same independent variable.

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Related Rates Problems 1

Related Rate Problems II

Good Question 9 Baseball and Related Rates

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 4.5 Solving Related Rate ProblemsLEARNING OBJECTIVECHA-3.E Interpret related rates in applied contexts. CHA-3.E.1 The derivative can be used to solve related rates problems; that is, finding a rate at which one quantity is changing by relating it to other quantities whose rates of change are known.

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Related Rates Problems 1

Related Rate Problems II

Good Question 9 Baseball and Related Rates

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 4.6 Approximating Values of a Function Using Local Linearity and LinearizationLEARNING OBJECTIVECHA-3.F Approximate a value on a curve using the equation of a tangent line. CHA-3.F.1 The tangent line is the graph of a locally linear approximation of the function near the point of tangency. CHA-3.F.2 For a tangent line approximation, the function’s behavior near the point of tangency may determine whether a tangent line value is an underestimate or an overestimate of the corresponding function value.

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Local Linearity The graphical manifestation of the derivative

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ENDURING UNDERSTANDING

LIM-4 L’Hospital’s Rule allows us to determine the limits of some indeterminate forms.

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 4.7 Using L’Hospital’s Rule for Determining Limits of Indeterminate FormsLEARNING OBJECTIVELIM-4.A Determine limits of functions that result in indeterminate forms. LIM-4.A.1 When the ratio of two functions tends to or in the limit, such forms are said to be indeterminate. LIM-4.A.2 Limits of the indeterminate forms or may be evaluated using L’Hospital’s Rule.

EXCLUSION STATEMENT: There are many other indeterminate forms, such as , for example, but these will not be assessed on either the AP Calculus AB or BC Exam. However, teachers may include these topics, if time permits.

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Unit 4 Contextual Applicationsap Calculus Answers

Determining the Indeterminate 1

Determining the Indeterminate 2 Same name, different post. Examining an implicit relation

Locally Linear L’Hôpital Demonstrating L’Hôpital’s Rule (a/k/a L’Hospital’s Rule)

Unit 4 Contextual Applicationsap Calculus 1

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