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# Unit 9: Parametric equations, polar coordinates, and vector-valued functions

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## About this unit

While we're often familiar with functions that output just one variable and are graphed with Cartesian coordinates, there are other possibilities! Vector-valued functions, for example, can output multiple variables. Polar functions, too, differ, using polar coordinates for graphing. We can still explore these functions with derivatives and integrals.

### Practice

- Parametric equations differentiationGet 3 of 4 questions to level up!

### Practice

- Second derivatives (parametric functions)Get 3 of 4 questions to level up!

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### Practice

- Parametric curve arc lengthGet 3 of 4 questions to level up!

Level up on the above skills and collect up to 240 Mastery points

### Learn

### Practice

- Vector-valued functions differentiationGet 3 of 4 questions to level up!
- Second derivatives (vector-valued functions)Get 3 of 4 questions to level up!

### Learn

### Practice

- Planar motion (differential calc)Get 3 of 4 questions to level up!
- Motion along a curve (differential calc)Get 3 of 4 questions to level up!
- Planar motion (with integrals)Get 3 of 4 questions to level up!

Level up on the above skills and collect up to 400 Mastery points

### Learn

### Practice

- Differentiate polar functionsGet 3 of 4 questions to level up!
- Tangents to polar curvesGet 3 of 4 questions to level up!

### Learn

### Practice

- Area bounded by polar curves introGet 3 of 4 questions to level up!
- Area bounded by polar curvesGet 3 of 4 questions to level up!

### Practice

- Area between two polar curvesGet 3 of 4 questions to level up!

### Practice

- Area with polar functions (calculator-active)Get 3 of 4 questions to level up!

Level up on the above skills and collect up to 480 Mastery points

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Level up on all the skills in this unit and collect up to 1,400 Mastery points!#### Unit test

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