What This Document Is
This document contains worked solutions for Exam Two from a Calculus II (MATH 132) course offered at Washington University in St. Louis, originally administered in Spring 2003. It’s a detailed, problem-by-problem breakdown intended to clarify the approaches and techniques used to tackle a variety of calculus concepts. The exam focuses on topics typically covered in a second semester of calculus, including integration techniques, applications of integration, and series.
Why This Document Matters
This resource is invaluable for students who have already attempted the exam and are looking to understand where they went wrong, or for those preparing to take a similar assessment. It’s particularly helpful for identifying common errors and solidifying understanding of core calculus principles. Students who benefit most are those actively engaged in a Calculus II course and seeking a deeper comprehension of exam-level problem solving. It’s best used *after* independent work on similar problems, as a tool for self-assessment and targeted review.
Common Limitations or Challenges
This document presents completed solutions; it does not offer step-by-step guidance for *how* to arrive at those solutions. It assumes a foundational understanding of Calculus II concepts. It also focuses specifically on the questions presented on *this particular* exam, and may not cover the full breadth of topics within the course. It’s important to remember that exam questions can vary, so relying solely on this resource won’t guarantee success on a future assessment.
What This Document Provides
* Detailed solutions for a variety of Calculus II problems.
* Coverage of topics including integration by substitution, radioactive decay modeling, partial fraction decomposition, and numerical integration using Simpson’s Rule.
* Analysis of improper integrals and their convergence/divergence.
* Applications of calculus to real-world scenarios, such as modeling radiation emission rates.
* Discussion of error estimation techniques in numerical integration.
* Worked examples relating to velocity, displacement, and calorie consumption modeling.
