Module 24 - Power Series
  Introduction | Lesson 1 | Lesson 2 | Lesson 3 | Self-Test
 Self Test

  1. The Maclaurin series for y = tan-1(x) is . What is the fifth-order Maclaurin polynomial for y = tan-1 (x)?
  2. Graph y = tan-1 (x) with a thick graphing style. In the same window graph the 5th-, 9th-, and 13th-order Maclaurin polynomials for this function. Estimate the interval of convergence for the series based on your graph.
  3. Find the second-order Taylor polynomial centered at 2 for y = ex.
  4. The second order Maclaurin polynomial for f(x) = ex is . Use this series to find the fourth-order Maclaurin polynomial for y = ex2 .
  5. Graph y = ex2 with a thick graphing style together with the fourth-order Maclaurin polynomial for y = ex2.

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