What This Document Is
This is a practice worksheet for Calculus II (MATH 132) at Washington University in St. Louis, specifically designed for a Peer-Led Team Learning (PLTL) session from Fall 2014. It focuses on the application of Taylor and Maclaurin series, convergence testing, and power series representations of functions. The worksheet is structured to encourage collaborative problem-solving and a deeper understanding of series concepts. It’s intended to be worked through in a group setting, reinforcing key ideas presented in lectures.
Why This Document Matters
This resource is ideal for students currently enrolled in a Calculus II course who are looking to solidify their understanding of infinite series. It’s particularly helpful for those who benefit from working through problems with peers and applying theoretical knowledge to concrete examples. Utilizing this worksheet can improve your ability to manipulate and analyze power series, determine intervals of convergence, and approximate function values using series representations. It’s best used *after* initial exposure to the concepts in class, as a way to actively practice and identify areas where further clarification is needed.
Common Limitations or Challenges
This worksheet does not provide a comprehensive review of all Calculus II topics. It concentrates specifically on Taylor and Maclaurin series and related convergence properties. It also doesn’t offer fully worked-out solutions; the intention is for students to actively engage with the problems themselves. While the PLTL structure suggests collaborative work, this resource doesn’t provide the benefit of direct interaction with a peer leader or classmates. Access to the full content is required to see the complete problem statements and develop solutions.
What This Document Provides
* Problems centered around finding Taylor series for given functions.
* Exercises involving the use of known series (like those for ln(1+x) and arctan(x)) to verify results.
* Practice determining the interval of convergence for various power series.
* Questions designed to assess understanding of the accuracy of series approximations.
* Tasks focused on constructing Maclaurin series for exponential functions and combinations thereof, expressed in summation notation.
* Problems categorized by suggested group work method (Scribe, Round Robin, Pairs).
