## Unit 2 - Limits

## 2.1 The Tangent Problem

This section introduces tangent and secant lines. On the video I did not actually draw the lines PQ because they make the sketch too complicated. You need to imagine that each secant line PQ that I talk about is a line on the sketch and, as Q gets closer to P the slope of the secant approaches the slope of the tangent line at P.

Please watch the video and then move onto the next section.

Video: 2.1 the tangent problem

Homework page: There is no homework for this section.

Please watch the video and then move onto the next section.

Video: 2.1 the tangent problem

Homework page: There is no homework for this section.

## 2.2 The Limit of a Function: Continuous

You will need to print the Properties of Limits information sheet before starting 2.2. Click on the red letters to the left and print the page.

This section introduces the idea of a limit. Functions can be continuous when there is no break in the function or discontinuous when there is a break in the function. This section explains continuous functions.

Please watch the video, print the homework page and complete the work and then check your work against the homework key.

Video: 2.2 the limit of a function - continuous

Homework page: calc 2-2 questions.pdf

Homework key: calc 2-2 key.pdf

This section introduces the idea of a limit. Functions can be continuous when there is no break in the function or discontinuous when there is a break in the function. This section explains continuous functions.

Please watch the video, print the homework page and complete the work and then check your work against the homework key.

Video: 2.2 the limit of a function - continuous

Homework page: calc 2-2 questions.pdf

Homework key: calc 2-2 key.pdf

## 2.3 The Limit of a Function: Discontinuous

A discontinuous function may or may not have a limit, depending upon if the point of discontinuity is a "hole" or an "asymptote". This section focuses on discontinuous functions that have a limit - those with a "hole".

Please watch the video, print the homework page and complete the work and then check your work against the homework key.

Video: 2.3 the limit of a function - discontinuous

Homework page: calc 2-3 questions.pdf

Homework key: calc 2-3 key.pdf

Please watch the video, print the homework page and complete the work and then check your work against the homework key.

Video: 2.3 the limit of a function - discontinuous

Homework page: calc 2-3 questions.pdf

Homework key: calc 2-3 key.pdf

## 2.4 The Limit of a Function: No Limit

This section is focuses on discontinuous functions that do not have a limit.

Please watch the video, print the homework page and complete the work and then check your work against the homework key.

Video: 2.4 the limit of a function - no limit

Homework page: calc 2-4 questions.pdf

Homework key: calc 2-4 key.pdf

Please watch the video, print the homework page and complete the work and then check your work against the homework key.

Video: 2.4 the limit of a function - no limit

Homework page: calc 2-4 questions.pdf

Homework key: calc 2-4 key.pdf

## 2.5 One-Sided Limits: Graphs

This section takes another look at discontinuous functions that do not have limits. The graphs will show that they can have limits when approached from only one side.

Please watch the video, print the homework page and complete the work and then check your work against the homework key.

Video: 2.5 one-sided limits - graphs

Homework page: calc 2-5 questions.pdf

Homework key: calc 2-5 key.pdf

Please watch the video, print the homework page and complete the work and then check your work against the homework key.

Video: 2.5 one-sided limits - graphs

Homework page: calc 2-5 questions.pdf

Homework key: calc 2-5 key.pdf

## 2.6 One-Sided Limits: Equations

This section looks at the equations of one-sided limits.

Please watch the video, print the homework page and complete the work and then check your work against the homework key.

Video: 2.6 one-sided limits - equations

Homework page: calc_2-6_questions.pdf

Homework key: calc 2-6 key.pdf

Please watch the video, print the homework page and complete the work and then check your work against the homework key.

Video: 2.6 one-sided limits - equations

Homework page: calc_2-6_questions.pdf

Homework key: calc 2-6 key.pdf

## 2.7 Equation 1 for Tangent Lines

There are two limit equations that can be used to find the equation of a tangent line. This section shows the first of these equations.

Please watch the video and then move onto the next section.

Video: 2.7 equation 1 for tangent lines

Homework page: The homework for this section will be included in 2.8.

Please watch the video and then move onto the next section.

Video: 2.7 equation 1 for tangent lines

Homework page: The homework for this section will be included in 2.8.

## 2.8 Equation 2 for Tangent Lines

This section shows the second limit equation the can be used to find the equation of a tangent line.

Please watch the video, print the homework page and complete the work and then check your work against the homework key.

Video: 2.8 equation 2 for tangent lines

Homework page: calc 2-8 questions.pdf

Homework key: calc 2-8 key.pdf

Please watch the video, print the homework page and complete the work and then check your work against the homework key.

Video: 2.8 equation 2 for tangent lines

Homework page: calc 2-8 questions.pdf

Homework key: calc 2-8 key.pdf

## Finish off the unit

When you have completed all the assigned work and reviewed it please see Mrs. Buck for your unit test.