Unit 2 focuses on the idea of a mathematical limit. It is a brand new concept for you that expands on your current understanding of slopes of lines and tangent lines. This is fundamental to the understanding of Calculus and will be the underlying theory behind something called Derivatives (Unit 3). Each section below will have several instructional videos for each part, including examples and their solutions. After all parts are completed within a section, there will be a set of questions to be done and handed in. After all sections are completed, there will be a single summative assessment (unit exam) covering all material from this unit.
Unit Sections a) The Tangent Problem i. Part One - The Tangent Problem ⇒ Teaching Video with Example Questions
There will be example questions within each video which students will be asked to do and then they will be walked through the solutions together. After all sub sections are done there will be a SINGLE FORMATIVE ASSESSMENT that students will complete and then submit. A walk through solutions video will then be given to the students to self assess their work.
b) The Limits of a Function i. Part One - The Limit of a Continuous Function ⇒ Teaching Video with Example Questions ii. Part Two - The Limit at a Discontinuous Part of a Function ⇒ Teaching Video with Example Questions iii. Part Three - The Limit Theorems ⇒ Teaching Video with Example Questions
There will be example questions within each video which students will be asked to do and then they will be walked through the solutions together. After all sub sections are done there will be a SINGLE FORMATIVE ASSESSMENT that students will complete and then submit. A walk through solutions video will then be given to the students to self assess their work.
c) Working with Limits i. Part One - Finding the Limit of Rational Functions Using Factoring ⇒ Teaching Video with Example Questions ii. Part Two - Find the Limit of Rational Expressions ⇒ Teaching Video with Example Questions iii. Part Three - Find the Limit of Radical Expressions ⇒ Teaching Video with Example Questions
There will be example questions within each video which students will be asked to do and then they will be walked through the solutions together. After all sub sections are done there will be a SINGLE FORMATIVE ASSESSMENT that students will complete and then submit. A walk through solutions video will then be given to the students to self assess their work.
d) One Sided Limits i. Part One - Right and Left Hand Limits ⇒ Teaching Video with Example Questions ii. Part Two - Piecewise Functions and Their Limits ⇒ Teaching Video with Example Questions
There will be example questions within each video which students will be asked to do and then they will be walked through the solutions together. After all subsections are done there will be a SINGLE FORMATIVE ASSESSMENT that students will complete and then submit. A walk through solutions video will then be given to the students to self assess their work.
e) Discontinuous Functions i. Part One - Formal Rules of Continuous Functions ⇒ Teaching Video with Example Questions
There will be example questions within each video which students will be asked to do and then they will be walked through the solutions together. After all sub sections are done there will be a SINGLE FORMATIVE ASSESSMENT that students will complete and then submit. A walk through solutions video will then be given to the students to self assess their work.
f) Using Limits to Find Tangents i. Part One - Finding the Slope of the Tangent Line at a Certain Value ⇒ Teaching Video with Example Questions ii. Part Two - Find the Formula for the Slope of a Tangent Line ⇒ Teaching Video with Example Questions
There will be example questions within each video which students will be asked to follow along with and write out. After all sub sections are done there will be a SINGLE FORMATIVE ASSESSMENT that students will complete and then submit. A walk through solutions video will then be given to the students to self assess their work.
g) Infinite Sequences i. Part One - Infinite Sequences ⇒ Teaching Video with Example Questions
There will be example questions within each video which students will be asked to do and then they will be walked through the solutions together. After all sub sections are done there will be a SINGLE FORMATIVE ASSESSMENT that students will complete and then submit. A walk through solutions video will then be given to the students to self assess their work
h) Infinite Series i. Part One - Infinite Series ⇒ Teaching Video with Example Questions
There will be example questions within each video which students will be asked to do and then they will be walked through the solutions together. After all sub sections are done there will be a SINGLE FORMATIVE ASSESSMENT that students will complete and then submit. A walk through solutions video will then be given to the students to self assess their work *There is a single summative assessment that concludes this unit.