What This Document Is
This document is a focused collection of problems designed to test your understanding of horizontal asymptotes within a Calculus I course. It centers on applying limit concepts to analyze the long-run behavior of various functions. The material appears to be geared towards practice and skill-building, likely stemming from older coursework ("OLD" is noted throughout). It emphasizes a specific approach to evaluating limits – one that *excludes* the use of a particular theorem commonly taught later in the course.
Why This Document Matters
This resource is ideal for students currently enrolled in Calculus I, particularly those preparing for quizzes or exams covering limits and asymptotic behavior. It’s especially valuable if your course is intentionally delaying the introduction of certain limit evaluation techniques. Working through these problems will strengthen your ability to determine how functions behave as their input approaches positive or negative infinity, a foundational skill for more advanced calculus topics. Students who struggle with algebraic manipulation of functions before taking limits will also find this helpful practice.
Common Limitations or Challenges
This document focuses *solely* on problem-solving. It does not include detailed explanations of the underlying theory of horizontal asymptotes, nor does it offer step-by-step solutions. It assumes you already have a working knowledge of limit notation and basic function types. Furthermore, it explicitly prohibits the use of a specific, powerful limit-solving rule, meaning you’ll need to rely on other methods. It's designed to be a practice tool, not a comprehensive learning guide.
What This Document Provides
* A series of problems requiring the determination of limits as x approaches infinity and negative infinity.
* Exercises involving the analysis of functions defined graphically.
* Problems focused on sketching functions that meet specific limit criteria.
* Practice with evaluating limits of rational functions with varying degrees of polynomial terms in the numerator and denominator.
* Problems requiring analysis of the sign of polynomial expressions over intervals.
* Exercises involving bounding a function and determining a limit based on those bounds.
