Calculus 1 - Limits and Continuity

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Limits of Square Roots, Fractions, Rational, Trigonometric and Absolute Value Functions.

9 students enrolled

What Will I Learn?

- They will learn how to evaluate limits and determine the continuity of a function.

Requirements

- Students should know the basics of Algebra and Precalculus before taking this course.

Description

This course is designed for high school and college students taking their first semester of calculus and who are learning limits and continuity. Here is a list of topics covered in this video.

1. Evaluating Limits Using a Data Table

2. Evaluating Limits Analytically Using Direct Substitution

3. Finding The Limit of Trigonometric Functions

4. Properties of Limits - Multiplication and Division

5. Evaluating Limits By Factoring - GCF, Difference of Perfect Squares & Sum of Cubes, & Factoring By Grouping

6. Limits With Square Roots and Radicals

7. Limits of Rational Functions and Fractions

8. Limits of Rational Functions With Square Roots

9. Limits of Special Trigonometric Functions - Sine, Cosine, and Tangent - Trigonometry

10. The Squeeze Theorem

11. Evaluating Limits Graphically

12. Limits and Piecewise Functions

Who is the target audience?

- Students who are currently taking calculus in high school or in college.

Compare to Other Calculus Courses

Curriculum For This Course

26 Lectures

03:59:50
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Start Here
26 Lectures
03:59:50

This video provides a basic introduction into limits. It explains how to find the limit analytically by using simple substitution.

Preview
03:00

This video explains how to evaluate a limit numerically using a data table.

Evaluating a Limit Numerically Using a Data Table

02:26

This video tutorial explains the process of evaluating limits analytically using direct substitution.

Evaluating Limits Analytically Using Direct Substitution

02:26

This video tutorial discusses how to find the limit of common trigonometric functions using the direct substitution technique.

Finding The Limit of Trigonometric Functions

02:51

This video explains how to evaluate limits using basic properties of limits such as multiplication, division, and exponents.

Properties of Limits

04:51

This video tutorial explains how to find the value of a limit by factoring. It explains how to factor trinomials with a leading coefficient of 1, factoring by grouping, removing the GCF - greatest common factor, difference of perfect squares, and sum of perfect cubes. The formulas and equations are provided. This video tutorial contains plenty of examples and practice problems.

Evaluating Limits By Factoring

11:34

This lesson explains how to evaluate a limit that contains square roots and radicals by multiplying the fraction by the conjugate of the numerator of the fraction.

Preview
04:56

This video explains how to evaluate the limit of a rational function in the form of a complex fraction by multiplying the numerator and denominator by the common denominator of the smaller fractions.

Preview
04:48

This video tutorial explains how to evaluate a function that is both rational and contains a radical or a square root within a fraction. You need to multiply the fraction by the conjugate of the numerator and by the common denominator of the two smaller fractions.

Limits of Rational Functions and Square Roots

11:41

This video lesson explains how to find the limit of special trigonometric functions involving sine, cosine, and tangent.

Preview
15:22

This video explains how to evaluate limits by applying the squeeze theorem.

The Squeeze Theorem

10:21

This lesson explains how to evaluate limits graphically.

Preview
11:31

This video explains how to find the limit of a piecewise function.

Piecewise Functions and Limits

08:25

This video tutorial explains how to evaluate the limit of an absolute value function.

Limits and Absolute Value Equations

17:43

This video lesson discusses the greatest integer function and how to evaluate it using number lines and with limits.

The Greatest Integer Function

15:48

This video tutorial discusses infinite limits that usually occurs with a rational function.

Infinite Limits Part 1

11:51

This video tutorial is continuation of the lecture entitled "infinite Limits Part 1".

Preview
12:34

This video lecture explains how to find the vertical asymptote of a rational function.

Vertical Asymptotes

04:37

This video lesson explains how to evaluate limits at infinity numerically which is equivalent to finding the horizontal asymptote.

Limits at Infinity and Horizontal Asymptotes

19:23

This video tutorial provides plenty of examples and practice problems of evaluating infinite limits at infinity.

Infinite Limits at Infinity

15:14

This video provides an introduction into continuity. It discusses three types of discontinuities - the hole, the jump discontinuity, and the infinite discontinuity. The hole is a removable discontinuity. The infinite and jump discontinuity are nonremovable discontinuities.

Introduction to Continuity

01:24

This video explains how to quickly identify points of discontinuity by finding the x values that make a function undefined.

Identifying Points of Discontinuity

05:42

This video explains the 3 step continuity test which is useful for determining if a piecewise function is continuous or discontinuous at a certain point. (1) The f(x) must be defined. (2) The limit must exists. (3) The limit must equal the function at that point. Those are the 3 conditions that must be met to prove that a function is continuous at a point.

3 Step Continuity Test

09:48

This video tutorial explains how to find the value of the constant that will make the piecewise function continuous at a point.

Making a Piecewise Function Continuous

06:01

This video explains the intermediate value theorem and gives examples of how to apply it in a typical calculus problem.

Intermediate Value Theorem

06:15

This video quiz contains 10 multiple choice questions on some of the lessons covered in this course.

Video Quiz

19:18

About the Instructor