Topics:

• Discussion of problems 1, 3, and 4 from the homework last time. These are important for making sure that you understand the concept of a limit. You may also want to view one or more videos from the resources for the concept of a limit.
• Using Desmos graphing calculator to graph functions, in particular piecewise-defined functions like in the homework problems 13 and 15. (We will look at problem 15 next time.) You can type in the pieces of the definition, followed by the inequality restrictions on x enclosed in braces, like this: \[y = x^2 – x + 1 \{x\le 3\}\]\[y= 2x+1 \{x>3\}\]Another method for piecewise-defined functions is given here. Don’t forget that even if you use Desmos, you need to consider the domain of your function, because the graphing calculator cannot show you if there are holes in the graph!

Homework:

• Log in to WeBWorK, following the instructions given on this page. Start reading and working in the Orientation assignment to learn about how WeBWorK works. You should also then start the assignment “LimitsIntroShort”: do at least problems 6 and 7.
• View some of the videos in the post Some Resources for the concept of a limit for more thorough understanding, if you like.
• Look for your invitation to join the Piazza discussion board – it will have been sent by “the Piazza Team”, not by me, and it will have been sent to the email address that is listed in Blackboard for you. Or you can go directly to the Piazza board and join using your City Tech email address.
• Don’t forget about the homework from the text book from last time!
• There will be a one-question quiz at the start of class next time. The quiz will be on the question of whether it is always true that \[\displaystyle \lim_{x\rightarrow 5}f(x)\] is equal to \[f(5)\]. Be prepared to give an example where this is not true!