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Calculus 1 - Limits and Continuity
Rating: 4.9 out of 5(139 ratings)
814 students

Calculus 1 - Limits and Continuity

Limits of Square Roots, Fractions, Rational, Trigonometric and Absolute Value Functions.
Created byOrganic Chemistry Tutor
Last updated 5/2017
English

What you'll learn

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

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Course content

1 section • 26 lectures • 3h 59m total length

  • Introduction to Limits3:00

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

  • Evaluating a Limit Numerically Using a Data Table2:26

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

  • Evaluating Limits Analytically Using Direct Substitution2:26

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

  • Finding The Limit of Trigonometric Functions2:51

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

  • Properties of Limits4:51

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

  • Evaluating Limits By Factoring11:34

    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.

  • Limits With Square Roots and Radicals4:56

    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.

  • Limits of Rational Functions and Fractions4:48

    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.

  • Limits of Rational Functions and Square Roots11:41

    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 Special Trigonometric Functions15:22

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

  • The Squeeze Theorem10:21

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

  • Evaluating Limits Graphically11:31

    This lesson explains how to evaluate limits graphically.

  • Piecewise Functions and Limits8:25

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

  • Limits and Absolute Value Equations17:43

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

  • The Greatest Integer Function15:48

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

  • Infinite Limits Part 111:51

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

  • Infinite Limits Part 212:34

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

  • Vertical Asymptotes4:37

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

  • Limits at Infinity and Horizontal Asymptotes19:23

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

  • Infinite Limits at Infinity15:14

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

  • Introduction to Continuity1:24

    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.

  • Identifying Points of Discontinuity5:42

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

  • 3 Step Continuity Test9:48

    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.

  • Making a Piecewise Function Continuous6:01

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

  • Intermediate Value Theorem6:15

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

  • Video Quiz19:18

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

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

This section covers the main topics that you will typically encounter on your first major calculus exam.  Learning limits is important because it ties in nicely with the second major topic taught in calculus which is Derivatives.  The derivative is a function that can tell you the instantaneous slope of a function at any x value.  You can also calculate the instantaneous slope of any function at any x value using limits and the average rate of change formula.  In this way, limits and derivatives are related.

Who this course is for:

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

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