What This Document Is
This document contains detailed worked solutions for a Calculus II (MATH 128) exam administered at Washington University in St. Louis in Fall 2003. It’s a comprehensive resource covering a range of topics typically found in a third semester of calculus, focusing on problem-solving techniques and detailed explanations. The exam assesses understanding of core concepts through a variety of question types.
Why This Document Matters
This resource is invaluable for students who have recently taken (or are preparing to take) a similar Calculus II exam. It’s particularly helpful for identifying areas of strength and weakness, understanding common approaches to different problem types, and reinforcing core concepts. Students can use this to review after completing their own exam, or as a study aid when preparing for future assessments. It’s designed to help solidify understanding of differential equations, applications of integration, and related concepts.
Common Limitations or Challenges
This document focuses *specifically* on the solutions to one particular exam. It does not provide a comprehensive review of all Calculus II topics, nor does it offer foundational explanations of the underlying principles. It assumes a base level of understanding of the course material. It will not substitute for attending lectures, completing homework assignments, or actively participating in study groups. The solutions presented are tailored to the specific questions asked on this exam and may not directly translate to all variations of similar problems.
What This Document Provides
* Detailed step-by-step solutions to each of the 20 questions on the exam.
* Coverage of topics including differential equations (including growth and decay models).
* Applications of integration to real-world scenarios, such as sales projections and equilibrium price calculations.
* Solutions involving logistic growth models and population dynamics.
* Problems related to continuous compounding and account balances.
* Applications of Taylor polynomials for approximation and average value calculations.
* Worked examples demonstrating techniques for finding long-term behavior of functions and populations.
