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Unit: 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!
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- Second derivatives (parametric functions)Get 3 of 4 questions to level up!
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- Parametric curve arc lengthGet 3 of 4 questions to level up!
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- Vector-valued functions differentiationGet 3 of 4 questions to level up!
- Second derivatives (vector-valued functions)Get 3 of 4 questions to level up!
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- 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!
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- 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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- 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!
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- Area between two polar curvesGet 3 of 4 questions to level up!
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- Arc length of polar curvesGet 3 of 4 questions to level up!
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- Area with polar functions (calculator-active)Get 3 of 4 questions to level up!
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