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Calculus BC · AP · Infinite Sequences and Series

CED focus

Finding Taylor or Maclaurin Series for a Function

This topic is assessed on the AP Exam.

Multiple-choice tips

  • Name the convergence test or Taylor degree before eliminating choices.
  • Name the convergence test before picking an MC answer.
  • Eliminate endpoint errors on interval-of-convergence choices.
  • On Taylor MC, match degree or center to the stem.
  • Distinguish nth-term test (divergence only) from convergence claims.

Free-response tips

  • Verify test conditions; check endpoints for interval of convergence.
  • State the test and verify its hypotheses for series convergence.
  • Show ratio/root steps for radius; test endpoints separately.
  • Write a Taylor polynomial with labeled center and degree.
  • Bound error with a remainder when accuracy is asked.

Common traps

  • Claiming convergence from nth-term test alone
  • Concluding convergence from nth-term test alone
  • Forgetting to test interval endpoints
  • Using a Taylor polynomial of wrong degree

Quick checklist

  • [ ] Can name and apply one convergence test correctly
  • [ ] Can find a Taylor polynomial about a given center
  • [ ] Can state what a remainder bound guarantees

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