What This Document Is
This document is a review sheet designed to prepare students enrolled in Iowa State University’s Calculus I (MATH 165) course for their first exam. It covers key concepts and problem types that are likely to appear on the assessment. It’s a focused resource for self-assessment and targeted study.
Why This Document Matters
This review is essential for students aiming to solidify their understanding of introductory calculus topics before Exam 1. It’s most valuable when used *in addition* to regular coursework – lectures, homework, and textbook readings. Students who are unsure of their grasp on limits, asymptotes, and the definition of a derivative will find this particularly helpful for identifying areas needing further attention.
Common Limitations or Challenges
This review sheet is not a substitute for a complete understanding of the course material. It provides practice problems and highlights important concepts, but it does not offer detailed explanations of *why* those concepts work. It also doesn’t cover every possible problem type that could appear on the exam. Students should not rely on this review as their sole study resource.
What This Document Provides
This review includes worked examples and practice problems covering:
* Calculating limits, including limits involving square roots and trigonometric functions.
* Identifying vertical and horizontal asymptotes of functions.
* Redefining functions to ensure continuity.
* Applying the definition of a derivative to find f’(2).
* Using differentiation rules to find derivatives.
* Finding the equation of a tangent line.
* Analyzing position, velocity, and acceleration functions.
* A conceptual sketch relating a function to its derivative.
This preview does *not* include complete solutions to all problems, nor does it provide detailed step-by-step explanations of the underlying calculus principles. It is intended to be a diagnostic tool, not a comprehensive lesson.