This is not the official version of this course website. If you are enrolled in the online section of this course, section 650, please view the lectures at owl.uwo.ca. The content here is incomplete.

Week 2 : Inverse functions and limits

Welcome to week 2 of calculus online. The workflow for this week is similar to last week's, work your way through the video lessons and solve the assigned problems. Please do not rely heavily on the solution manual if you have it. If you have difficulty with the assigned problems it is much better to look through the video lessons for a similar problem and mimic the solution than to look up the solution manual.

By the end of this week you should be able to :

- understand the notion of limit
- compute limits, including one side and infinite limits
- recall the limit laws
- compute limits using the limit laws

Topic | Est. video completion time. | Textbook practice problems | |
---|---|---|---|

1 | Limits | 15 mins | Section 2.2 : 1, 2, 5, 7, 9, 11 |

2 | Infinite limits | 10 mins | Section 2.2 : 31-41 (odd) |

3 | Limit laws I | 10 mins | Section 2.3 : 1, 3-9 (odd), 11-31 (odd) |

4 | Limit laws II | 15 mins | Section 2.3 : 37, 39, 41, 43, 49, 53, 54 |

1. Limits

By the end of this lesson you should be able to :

- understand piecewise defined functions
- explain the intuitive definition of limit
- use the intuitive definition of limit to compute limits and one-sided limits

Once you have viewed the video complete the following problems from the textbook, Section 2.2 : 1, 2, 5, 7, 9, 11

Notes:

2. Infinite limits

By the end of this lesson you should be able to :

- State what it means for a limit to approach \(\pm \infty\).
- Compute infinite limits

Once you have viewed the video complete the following problems from the textbook, Section 2.2 : 31-41 (odd)

Notes:

3. Limit laws I

By the end of this lesson you should be able to :

- recall and apply the limit laws introduced in the video
- compute a limit by factoring and algebraic manipulation
- compute a limit by multiplying through by the conjugate of an expression

Once you have viewed the video complete the following problems from the textbook, Section 2.3 : 1, 3-9 (odd), 11-31 (odd)

Notes:

4. Limit laws II

By the end of this lesson you should be able to :

- recall and apply the squeeze theorem
- compute limits by dividing them into two one sided limits
- express a function involving an absolute value as a piecewise defined function
- describe the greatest integer less than function
- compute limits involving the greates integer less than function

Once you have viewed the video complete the following problems from the textbook, Section 2.3 : 37, 39, 41, 43, 49, 53, 54

Notes: