patty's calculus videos

part 1 - limits and continuity (12 videos)                      back to playlists

Part 1 - Limits and Continuity - Video 1
Section 1: The Limit of a Function
Lesson 1 (42:46)

In this lesson we explore the concept of the limit of a function, first finding the limit using a table of values (4:23). Next we find the limit of a function from its graph (21:00).

Part 1 - Limits and Continuity - Video 2
Section 1: The Limit of a Function
Lesson 2 (48:56)

In this lesson we learn about one-sided limits, finding these from the graph (0:40). Next we find one-sided limits of a piecewise function from its equation (26:00).

Part 1 - Limits and Continuity - Video 3
Section 1: The Limit of a Function
Lesson 3 (24:06)

In this lesson we learn about limits that go to infinity, first by looking at a specific example (0:40). Next we discuss the definition of a limit that goes to infinity for a general function (12:00).

Part 1 - Limits and Continuity - Video 4
Section 2: Calculating Limits
Lesson 1 (53:49)

We develop the limit laws by exploring two building block limits (0:40). Next we discuss the sum, difference, constant multiple, product, and quotient limit laws (17:16). We work an example using these laws (35:18).

Part 1 - Limits and Continuity - Video 5
Section 2: Calculating Limits
Lesson 2 (1:01:06)

First we discover how to find the limit of a polynomial function (0:40), then of a rational function (10:45). We deal with examples in which we can't use direct substitution to find the limit (17:12).

Part 1 - Limits and Continuity - Video 6
Section 2: Calculating Limits
Lesson 3 (57:53)

We begin this lesson by finding the limit of a piecewise function from its equation (0:40). Next we look at an example of a piecewise function involving the absolute value of x (11:34).

Part 1 - Limits and Continuity - Video 7
Section 3: Continuity
Lesson 1 (56:29)

Intuitive definition of continuity (0:35). Develop a precise definition of continuity by seeing how a function might not be continuous (8:02). Last, apply this precise definition to two examples (33:27).

Part 1 - Limits and Continuity - Video 8
Section 3: Continuity
Lesson 2 (55:27)

We complete the previous lesson by applying the precise definition of continuity to a third example (0:30). We discuss different types of discontinuity, including removable versus non-removable (11:11).

Part 1 - Limits and Continuity - Video 9
Section 3: Continuity
Lesson 3a (49:00)

We discuss continuity on an interval (0:27). Next we determine where a function is continuous from its equation instead of its graph (19:50). Specifically, we discuss the continuity of polynomials (28:50), and of rational functions (35:52).

Part 1 - Limits and Continuity - Video 10
Section 3: Continuity
Lesson 3b (51:27)

We continue to learn how to determine the continuity of a function from its equation, by discussing the continuity of functions containing roots (general algebraic functions).

Part 1 - Limits and Continuity - Video 11
Section 3: Continuity
Lesson 4a (47:27)

We determine the continuity of a function from its equation, using the continuity of trig functions (0:30). Next, continuity of inverse functions (21:14), to determine where the inverse trig functions are continuous (25:14).

Part 1 - Limits and Continuity - Video 12
Section 3: Continuity
Lesson 4b (49:15)

We use equations of combinations of functions in specific examples (0:40). We discuss the continuity of the composition of two functions (13:04), and work two examples (16:15). Last, the continuity of one of our weird functions (27:36).