What This Document Is
This document is a comprehensive final examination for a Calculus II (MATH 128) course at Washington University in St. Louis. It’s designed to assess a student’s understanding of the core concepts covered throughout the semester, focusing on multi-variable calculus and related techniques. The exam format includes a variety of problem types, requiring both computational skills and conceptual understanding.
Why This Document Matters
This resource is invaluable for students currently enrolled in Calculus II, or those preparing to take the course. It’s particularly useful for final exam review, allowing students to gauge their preparedness and identify areas needing further study. Working through practice problems similar in style and difficulty to those presented here is a proven strategy for exam success. It can also be beneficial for instructors seeking examples of assessment questions.
Common Limitations or Challenges
This document presents the *questions* from a past final exam, but does not include detailed solutions or step-by-step explanations. It serves as a practice tool, but won’t teach you the underlying concepts. Students should have a solid foundation in Calculus II principles before attempting to work through these problems. Access to course notes, textbooks, and potentially supplemental learning materials will be essential for fully benefiting from this resource.
What This Document Provides
* A collection of problems covering key Calculus II topics, including partial derivatives and implicit differentiation.
* Questions assessing understanding of linearization and tangent plane equations.
* Problems focused on critical point analysis of multi-variable functions.
* Optimization problems involving constraints, utilizing techniques like Lagrange multipliers.
* A range of multiple-choice questions designed to test conceptual understanding and problem-solving abilities.
* Problems relating to functions of multiple variables and their minimum/maximum values.
* Questions involving linear programming and feasible regions.
