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Unit 4: Contextual Applications of the Differentiation

AP Calculus AB/BC

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Presentation Slides, L'Hospital's Rule

Browse slides from the stream 'L'Hospital's rule.'

L'Hospital's rule

This stream reviews L'Hospital's rule, when to use it, and how to use it. We review examples of how to use L'Hospital's rule for free response questions. We will go over examples where you could use L'Hospital's rule but it can make it a bit more complicated!

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4.0 Unit 4 Overview: Contextual Applications of Differentiation

Now that you have mastered the rules and formulas of differentiation, it is time for us to apply them! This section focuses on taking all the previous derivative rules and applying them in different contexts.

Related Rates

In real world examples one thing changes and that affects how other related things change. By building an equation and differentiating we can relate the two changing quantities.

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4.1 Interpreting the Meaning of the Derivative in Context

While we use the word derivative in calculus, it is important to know that we are just talking about the slope at a point! In real-world situations, there are different ways that the idea of a derivative can be interpreted to us.

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4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration

One way we apply derivatives to real life through rates of change involves position and motion. These problems involve rectilinear motion. 🚗

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4.3 Rates of Change in Applied Contexts other than Motion

While the title says “Other Than Motion,” really all rates of change are talking about something being in motion. It may not directly say something is in motion but is talking about a change in some way that involved something moving.

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4.4 Intro to Related Rates

🎥Watch: AP Calculus AB/BC - Related Rates

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4.5 Solving Related Rates Problems

🎥Watch: AP Calculus AB/BC - Related Rates

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4.6 Approximating Values of a Function Using Local Linearity and Linearization

In this section, the equation of the tangent line is very important! We are going to find an equation of a tangent line at a point, but then plug in another x or y value and use the tangent line at one point to approximate a point very close to it. 🤩

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4.7 Using L'Hopitals Rule for Determining Limits in Indeterminate Forms

Remember those times when you were solving limits at infinity, and you would come out with an answer that looked like ♾️/♾️ or 0/0, and you would have to see if there was another way to manipulate the equation or cancel out some terms to try and find an answer that was not in an indeterminate form?

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Free Review 2020

18 resources

Free Response Questions (FRQ)

10 resources

Unit 1: Limits & Continuity

24 resources

Unit 2: Differentiation: Definition & Fundamental Properties

19 resources

Unit 3: Differentiation: Composite, Implicit & Inverse Functions

16 resources

Unit 4: Contextual Applications of the Differentiation

11 resources

Unit 5: Analytical Applications of Differentiation

17 resources

Unit 6: Integration and Accumulation of Change

7 resources

Unit 7: Differential Equations

10 resources

Unit 8: Applications of Integration

16 resources

Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)

11 resources

Unit 10: Infinite Sequences and Series (BC Only)

16 resources

Multiple Choice Questions (MCQ)

1 resource

Blogs

16 resources

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