Limits and Derivatives in Calculus 1 by Infinite Wisdom

Name: Limits and Derivatives in Calculus 1 by Infinite Wisdom
Rating: 5.0 (1 reviews)

Understand limits and derivatives from Calculus 1 and be able to solve challenging problems

Created byNicole Southern

Last updated 3/2025

English

What you'll learn

Be able to solve challenging limit and derivative problems
Improve your grade in your Calculus I course
Understand limits and derivatives from a graphical, numerical, and algebraic perspective
Improve your grade in your Calculus 1 or AP Calculus course

Course content

3 sections • 22 lectures • 2h 40m total length

Introduction to Infinite Wisdom1:09

Limits from Graphs5:00
Watch this video to get a general introduction to the concept of a limit.
Basic Limits8:47
Use the first attached worksheet to follow along while we solve these limits problems together in the video. Then, try the second worksheet on your own and check your answers using the attached solutions.
Numerical Limits and Mixed Practice4:54
Watch the video and follows along on the attached worksheet. Then, try the attached worksheet to monitor your understanding of limits and then check your understanding using the answer key.
Knowing Your Graphs7:55
1. Watch Know Your Graphs Video and follow along, if you like, with the Know Your Graphs Video worksheet.
2. Try Know Your Graphs Practice and check your solutions using Know Your Graphs - Solutions.
Limits of Piece-Wise Functions5:01
Watch the video and follow along using the attached worksheet. Then, make sure you practice using the attached worksheet and be sure to check your answers.
Finding Limits Algebraically10:39
Watch video and follow along with accompanying worksheet. Then, try the practice problems and carefully check your solutions.
Limits Involving Trigonometry6:19
1. Watch Limits Involving Trigonometry Videos 1 AND 2
2. You can follow along, if you choose, on the accompanying sheets if you like to take notes on them. Also attached are the trig identities that you need to know for this course.
3. Complete the Trig Limits Practice Worksheet and carefully check your solutions
Limits Involving Infinity11:03
1. Watch the video reviewing horizontal asymptotes FIRST. Then, watch the video on Limits Involving Infinity.
2. Try the practice problems and check your work by looking at the answer key.
Continuity7:37
1. Watch the continuity video and follow along on the accompanying sheet.
2. Try the practice problems and check your solutions.
Properties of Limits6:41
Watch the video on Limit Properties, look at the reference sheet used in the video, try the practice problems and then be sure to check your solutions and watch the solution video.
Intermediate Value Theorem8:17
Watch the video on the IVT and follow along with the accompanying video sheet. Then, complete the practice problems and be sure to check your solutions using the video explanations.
The Squeeze Theorem8:33
Unit Review: Limits and Continuity0:10

Lecture 15: Average rates of Change7:41
Watch the video and use the accompanying sheet to follow along. Then, try the practice problems and check your answers using the key.
Lecture 16: Instantaneous Rates of Change and the Def of the Derivative8:32
In these two videos you will learn the definition of the derivative in general and be able to practice using the worksheets and check answers with the key.
Lecture 17: The Derivative of a Function at a Point and Tangent and Normal Line7:47
Watch all three videos and then try BOTH practice sheets and check BOTH answer keys.
Lecture 18: The Power Rule9:19
Watch the proof video and other video. Don’t worry if it’s tough to follow the proof video. Then, practice using the worksheets, as usual.
Lecture 19: Differentiability and Continuity10:15
Lecture 20: Basic Derivative Rules10:54
After you watch the video and use the follow along, there is mid-unit practice to check your comprehension up until this point in the unit.
Lecture 21: More Derivative Rules5:25
Watch all three videos, follow along with the accompanying sheet, then practice and check your answers.
Lecture 23: More Trig Derivatives8:07

Requirements

Proficient in Pre-Calculus and Algebra especially graphing functions, trigonometry, and algebraic manipulation

Description

Limits and Derivatives are a fundamental concept in Calculus. In order to thrive in the study of Calculus 1 and beyond, it is crucial to have a conceptual understanding of this topic. In this course, we will explore limits and derivatives graphically, numerically, algebraically and analytically. Every lesson contains a lecture with an accompanying follow along sheet, practice problems with solutions given in video and written format, formula sheets, and an extensive set of review problems at the end of the course along with an answer key.

List of lessons:

Finding Limits from Graphs
Numerical Limits from Tables
Know Your Graphs
Limits of Piecewise Functions
Algebraic Limits
Trigonometric Limits
Infinite Limits
Continuity
Limit Properties
Intermediate Value Theorem
Unit 1 Review

Average Rates of Change
The Definition of the Derivative and Instantaneous Rates of Change
The Derivative of a Function at a Point plus Tangent and Normal Lines
The Power Rule
Differentiability and Continuity
Basic Derivative Rules
More Derivative Rules
The Product and Quotient Rules
Trigonometric Derivatives

This course is intended for a variety of high school and college students who have already taken Precalculus. It is perfect for students who want to get a jump start and preview the first two units of Calculus before they begin then course. It is equally ideal for students who are currently taking Calculus 1 or AP Calculus AB or BC and feel that they are not totally understanding the material being taught by their teacher. The course may be used as a refresher for students who took Calculus a while ago and need to re-master the early concepts.

The other units in Calculus 1 will be posted very shortly!

Who this course is for:

High school students taking AP Calculus AB and BC
College students taking Calculus 1
Any student looking to preview the early content of Calculus
Students who need a refresher on limits and derivatives for another course

Limits and Derivatives in Calculus 1 by Infinite Wisdom

What you'll learn

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Course content

How to Best Utilize this Course1 lecture • 1min

Unit 1: Limits and Continuity13 lectures • 1hr 31min

Unit 2: The Definition of the Derivative and Basic Derivative Rules8 lectures • 1hr 8min

Requirements

Description

Who this course is for: