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Calc BC Unit 9-11

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68 views1 page

Calc BC Unit 9-11

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leozhang233
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Unit 9: Series and Sequences

●​ Sequences: Ordered lists of numbers.


○​ Example: 1, 2, 4, 8, ...
●​ Series: Sums of sequences.
○​ Example: 1 + 2 + 4 + 8 + ...
●​ Convergence and Divergence: Tests for determining whether a series converges or
diverges.
○​ Example: Geometric Series, p-Series, Ratio Test

Unit 10: Power Series


●​ Power Series: Series of the form ∑a_n(x-c)^n.
○​ Example: 1 + x + x^2 + x^3 + ...
●​ Taylor Series: Power series expansions of functions around a point.
○​ Example: e^x = 1 + x + x^2/2! + x^3/3! + ...
●​ Maclaurin Series: Taylor series expansions around x=0.
○​ Example: sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ...

Unit 11: Parametric and Polar Equations (Review)


●​ Parametric Equations: Equations that define a curve using a parameter.
○​ Example: x = t^2, y = 3t
●​ Polar Equations: Equations that define a curve using polar coordinates.
○​ Example: r = 2cosθ

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