Evaluating Limits

Explore the fundamental concepts of calculus in this comprehensive 2.5-hour tutorial on evaluating limits. Begin with an introduction to Zeno's Paradox and progress through the definition of limits, right- and left-hand limits, and vertical asymptotes. Examine trigonometric functions like tan(x) and sec^2(x), and analyze asymptotes in rational functions. Master the limit laws and their applications to polynomials and rational functions. Delve into the Squeeze Theorem and continuity, including its properties and potential failures. Conclude with an exploration of the Intermediate Value Theorem, gaining a solid foundation in calculus principles and problem-solving techniques.

Syllabus

Intro to Calculus: Zeno's Paradox.
Definition of the Limit.
Right- and Left-hand Limits.
tan(x) & Vertical Asymptotes.
More Vertical Asymptotes: sec^2(x).
Asymptotes of a Rational Function.
A Nasty Rational Function.
The Limit Laws.
Limit Laws & Polynomials.
Limit Laws & Rational Functions.
Squeeze Theorem.
Continuity: 3 ways it fails.
Continuity: Two Examples.
Continuity: Properties.
Intermediate Value Theorem.