What This Document Is
This document provides essential information for students preparing for Exam 2 in MATH 220, Calculus, at the University of Illinois at Urbana-Champaign. It’s a comprehensive overview designed to help you focus your study efforts and understand the scope of the assessment. This isn’t a substitute for attending lectures or completing assignments, but a valuable tool to clarify expectations and ensure you’re well-prepared.
Why This Document Matters
This resource is particularly helpful for students who want a clear understanding of the specific concepts and skills that will be tested on Exam 2. It’s best used in the days leading up to the exam as a final review guide, helping you prioritize topics and identify areas where you may need further study. Students who utilize this information alongside their notes and completed work will be best positioned for success.
Topics Covered
* Differentiation rules for various functions (polynomial, trigonometric, exponential, logarithmic)
* Implicit differentiation techniques
* Logarithmic differentiation methods
* Applications of derivatives: tangent lines, velocity, acceleration
* Exponential growth and decay models, including half-life calculations
* Related rates problems and relevant geometric formulas
* Analysis of functions: critical points, increasing/decreasing intervals, concavity, inflection points
* Optimization problems and the Extreme Value Theorem
* Limit calculations, including indeterminate forms and L'Hôpital’s Rule
What This Document Provides
* A clear outline of the specific sections from the course textbook that will be covered on the exam.
* A list of key derivative rules you are expected to know and apply.
* Guidance on the types of application problems related to rates of change and function analysis that may appear on the exam.
* Reminders of important theorems and concepts related to function behavior and limit evaluation.
* References to relevant course materials, such as worksheets, quizzes, homework solutions, and previous tests.
* Important logistical details regarding the exam itself, such as permitted materials and location.
