TBIL-Cal Power Series (PS)

Chapter 9 Power Series (PS)

How do we use series to understand functions?

By the end of this chapter, you should be able to...

Approximate functions defined as power series.
Determine the interval of convergence for a given power series.
Compute power series by manipulating known exponential/trigonometric/binomial power series.
Determine a Taylor or Maclaurin series for a function.

Before beginning this chapter, you should be able to...

Compute limits.
- Review: Khan Academy
  ¹
  https://www.khanacademy.org/math/ap-calculus-bc/bc-limits-new/bc-1-2/v/introduction-to-limits-hd?modal=1
- Review: Khan Academy
  ²
  https://www.khanacademy.org/math/ap-calculus-bc/bc-diff-contextual-applications-new/bc-4-7/v/introduction-to-l-hopital-s-rule?modal=1
Express the sum of indexed values using summation notation.
- Review: Khan Academy
  ³
  https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/v/sigma-notation-sum
Employ the ratio test for convergence.
- Review: Khan Academy
  ⁴
  https://www.khanacademy.org/math/ap-calculus-bc/bc-series-new/bc-10-8/v/ratio-test-convergence
Power rule for differentiating and integrating.
- Review: Khan Academy
  ⁵
  https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-5/v/power-rule
- Review: Khan Academy
  ⁶
  https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8a/v/indefinite-integrals-of-x-raised-to-a-power