Topics:
• Notation for limits and one-sided limits
• Properties of limits
A slightly improved version of the notes I handed out in class is here:
The substitution property says that for certain types of functions, as long as c is a number in the domain of that function, it will be true that $\displaystyle \lim{x\rightarrow c}f(x) = f(c)$
There are some other functions which have the substitution property in addition to polynomials and rational functions. Here are some that you know from previous math classes:
The trig functions $\sin(x)$, $\cos(x)$, $\tan(x)$, $\cot(x)$, $\sec(x)$, $\csc(x)$
The exponential function $b^{x}$ for any positive base $b$ ($b\neq 1)
The logarithmic function $\log_b(x)$ for any positive base $b$ ($b\neq 1)
In particular, the functions $e^x$ and $\ln(x)$ have the substitution property.
We use the properties of limits to shortcut the process of finding a limit whenever possible from now on. We will have to resort to other means when these properties cannot be used, though.
Homework:
• If you have not already joined Piazza: Look for the invitation to join our Piazza discussion board, and join by following the link. The invitation has been sent to whatever email address you have in Blackboard, and it will be from “The Piazza Team”. Or you can go directly to Piazza here and join using your City Tech email address. We will be using the discussion board as a way to ask questions about the homework or the material discussed in class.
• Last call: If you have not already done so, log in to WeBWorK following the instructions here (which were also handed out in class) and make sure to enter your City Tech email! (If you do not yet have a City Tech email, please enter it as soon as possible.) You must have your City Tech email address in your User information in WeBWorK in order to be able to use the “email your instructor” feature, and also it will be used to send out your midterm grades.
• Do the WeBWorK assignment “Limits-Continuity1”. For people who joined this class this week, you still have some time to work on the previous assignment as well. Make sure that you follow the instructions given in the homework assignment last time.
• Also do the following problems from the textbook: p. 28 #7-13 odd, 19-25 odd. I may ask for volunteers to put some of these on the board.
• Monday 12 February is a holiday (no classes meet).
• There will be a Quiz on Wednesday. The question will be a randomly selected homework problem from today’s assignments.
Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question. And please only put one problem per posted question!
Note on my schedule: for the time being, I will only be able to be online to read and reply to emails at certain times of the day. (It is possible that I may be online at other times but I cannot guarantee it.) The times are roughly:
Monday – Friday early morning
Monday-Thursday around 2:30-3:00 PM
Sunday-Thursday evenings around 9-10 PM
Please be aware of this if you need to contact me by email. Thanks.
