AI Summary
[DOCUMENT_TYPE: exam_prep]
**What This Document Is**
This document contains a complete solution set for Exam Two from Math 128, Calculus II, offered at Washington University in St. Louis during the Fall 2009 semester. It’s a detailed walkthrough intended to reinforce your understanding of the course material as it was assessed on that specific exam. The document presents responses to a variety of problems covering key concepts from the second portion of the Calculus II curriculum.
**Why This Document Matters**
This resource is invaluable for students who have already attempted Exam Two and are looking to thoroughly review their performance. It’s particularly helpful for identifying areas where understanding may be incomplete or where specific calculation errors occurred. Studying worked solutions can solidify your grasp of complex techniques and improve your problem-solving skills for future assessments. It’s best used *after* independent effort has been made to solve the exam problems, as simply reviewing solutions without prior attempt can hinder true learning.
**Common Limitations or Challenges**
This document focuses *solely* on the solutions to the Fall 2009 Exam Two. It does not include explanations of the underlying concepts, derivations of formulas, or alternative approaches to problem-solving. It assumes you have a foundational understanding of Calculus II principles. Furthermore, it doesn’t offer personalized feedback on your own work – it simply presents the expected answers as determined by the course instructor. Accessing this document will not substitute for attending lectures, completing homework assignments, or seeking help during office hours.
**What This Document Provides**
* Detailed responses to each of the 20 questions on the exam.
* Solutions addressing topics such as homogeneous functions.
* Applications of linear approximation techniques.
* Calculations related to tangent planes for various surfaces.
* Methods for finding points on planes closest to the origin.
* Analysis of stationary points and classifications of critical points for multivariable functions.
* Exploration of differentials of composite functions.
* Problem sets covering a range of Calculus II concepts.