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Unit 12: Power series

About this unit

Power series are infinite series of the form Σaₙxⁿ (where n is a positive integer). Even though this family of series has a surprisingly simple behavior, it can be used to approximate very elaborate functions.

Power series intro

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Power series intro
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Worked example: interval of convergence
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Integrating power series
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Differentiating power series
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Interval of convergence for derivative and integral
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Practice

Interval of convergence
4 questions
Integrate & differentiate power series
4 questions

Taylor & Maclaurin polynomials intro

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Taylor & Maclaurin polynomials intro (part 1)
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Taylor & Maclaurin polynomials intro (part 2)
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Worked example: Maclaurin polynomial
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Worked example: coefficient in Maclaurin polynomial
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Worked example: coefficient in Taylor polynomial
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Taylor polynomial remainder (part 1)
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Taylor polynomial remainder (part 2)
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Worked example: estimating sin(0.4) using Lagrange error bound
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Worked example: estimating eˣ using Lagrange error bound
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Visualizing Taylor polynomial approximations
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Worked example: Taylor polynomial of derivative function
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Practice

Taylor & Maclaurin polynomials
4 questions
Lagrange error bound
4 questions

Maclaurin series of sin(x), cos(x), and eˣ

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Maclaurin series of cos(x)
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Maclaurin series of sin(x)
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Maclaurin series of eˣ
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Euler's formula & Euler's identity
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Worked example: power series from cos(x)
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Worked example: cosine function from power series
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Worked example: recognizing function from Taylor series
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Visualizing Taylor series approximations
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Practice

Maclaurin series of sin(x), cos(x), and eˣ
4 questions

Power series function representation

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Function as a geometric series
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Geometric series as a function
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Geometric series interval of convergence
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Power series of arctan(2x)
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Power series of ln(1+x³)
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Finding function from power series by integrating
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Practice

Function as a geometric series
4 questions
Integrals & derivatives of functions with known power series
4 questions

Challenge series exercises

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Practice

Convergence tests challenge
7 questions
Series estimation challenge
7 questions
Taylor, Maclaurin, & Power series challenge
7 questions

Unit 12: Power series

About this unit

Power series intro

Learn

Practice

Taylor & Maclaurin polynomials intro

Learn

Practice

Maclaurin series of sin(x), cos(x), and eˣ

Learn

Practice

Power series function representation

Learn

Practice

Challenge series exercises

Learn

Practice

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