What This Document Is
This is a practice worksheet designed to reinforce core concepts from Washington University in St. Louis’ Calculus II (MATH 132) course, specifically focusing on the topic of series. It’s part of a Peer-Led Team Learning (PLTL) session from Fall 2014, meaning it’s structured around collaborative problem-solving and conceptual understanding. The worksheet delves into power series, Taylor polynomials, and convergence tests – essential building blocks for advanced calculus and related fields.
Why This Document Matters
This resource is ideal for students currently enrolled in a Calculus II course, or those reviewing series concepts in preparation for further study in mathematics, physics, or engineering. It’s particularly helpful for students who benefit from working through problems in a group setting and solidifying their understanding through explanation and discussion. Use this worksheet to test your grasp of key definitions and theorems *before* an exam, or to identify areas where you need further clarification from your instructor. It’s designed to help you move beyond rote memorization and develop a deeper, more intuitive understanding of infinite series.
Common Limitations or Challenges
This worksheet does not provide fully worked-out solutions. It’s intended to be a tool for *active* learning, requiring you to apply your knowledge and reasoning skills. While hints are provided for some problems, the primary focus is on your ability to independently analyze and solve the presented challenges. It also assumes a foundational understanding of differentiation and integration, as well as basic series concepts covered earlier in the course. This is not a substitute for attending lectures or reading the textbook.
What This Document Provides
* Conceptual questions designed to assess your qualitative understanding of power series – including their definition, interval of convergence, and radius of convergence.
* Problems requiring you to determine the interval and radius of convergence for given power series.
* Exercises focused on Taylor polynomials, including calculating coefficients and using them for approximation.
* Practice applying convergence tests (like the Integral Test) to determine whether a series converges or diverges.
* Comparative analysis of different series and their convergence properties, requiring you to utilize various tests and techniques.
