Calculus 1: Limit

Summary

An introduction to the definition of limits in Calculus 1, including the Epsilon-Delta definition, property laws, the squeeze theorem, one-sided limits, continuity, and horizontal/vertical asymptotes.

Highlights

Limits Involving Infinity01:17:33

Explaining limits where values go to positive or negative infinity, leading to the identification of vertical asymptotes.

Horizontal and Slant Asymptotes01:45:38

Defining horizontal asymptotes based on limits at infinity and identifying slant asymptotes where function behavior mirrors a linear function.

One-Sided Limits00:39:54

Defining left-hand and right-hand limits and the condition required for a limit to exist (both sides must be equal).

Continuity of Functions00:57:50

Three conditions for continuity: the function is defined at x0, the limit exists, and the limit equals the function value.

Introduction to Limit Definitions00:00:00

Explanation of the formal Epsilon-Delta definition of a limit, describing how a function approaches a value L as X approaches x0.

Sequence-Based Definition00:06:03

Defining limits using sequences: if every sequence Xn converging to x0 implies f(Xn) converges to L, then the limit exists.

Limit Properties and Laws00:15:05

Overview of basic limit laws including sum, difference, product, and quotient rules, and applying them to polynomial functions.

The Squeeze Theorem00:21:04

Introduction to the Squeeze Theorem, used to find limits by trapping a function between two others that converge to the same value.