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# Unit 5: Parametric equations, polar coordinates, and vector-valued functions

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## About this unit

We are used to working with functions whose output is a single variable, and whose graph is defined with Cartesian, i.e., (x,y) coordinates. But there can be other functions! For example, vector-valued functions can have two variables or more as outputs! Polar functions are graphed using polar coordinates, i.e., they take an angle as an input and output a radius! Learn about these functions and how we apply the concepts of the derivative and the integral on them.

### 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!

Level up on the above skills and collect up to 160 Mastery points

### 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 240 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!

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### 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!

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### Practice

- Arc length of 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 560 Mastery points

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