Welcome to Calculus I!

Take a look around this website to see what resources are here. I am still adding things!

Before and after every class meeting, there will be a post of the day that contains notes, links to related materials, and details of what your homework assignment is for that day. Always check the blog post before heading off to WeBWorK, for example. (There will be a link to the WeBWorK when it is assigned, next time.

My course policies are on a separate page here.

In the future there will be separate pages for solutions to the Quizzes and for the Test Review problems sets.

Topics for today’s class:

• The idea of a limit: estimating limits by using a graph or tabulating values of the function.

• Three ways that a limit may fail to exist.

• Difference quotients and limits of difference quotients:

The idea is that the difference quotient represents the slope of a secant line through two nearby points – physically it represents the average rate of change of the function between those two x-values. We will be trying to find the slope of a tangent line to the graph at one point (an instantaneous rate of change) by making the points get closer and closer together, and see if the slopes of the secant lines approach a limit as we do so.

I hope to give more detailed notes (and using math notation) once I have a bit more time.

Homework:

• Download the textbook (or anyway Volume 1)  from this site:

http://www.apexcalculus.com/downloads

• Review the material we discussed in class, which is basically Section 1.1 in the textbook. Make sure that you understand the concept of a limit, the three ways a limit may fail to exist, and how to compute a difference quotient. (I prefer to compute the difference quotient as I did in class, by first computing f(x+h), then subtracting f(x) from that, and finally dividing by h. Note that we do not cancel out the common factor of h, because we are looking to see if there is a limit as h approaches 0.)

• Do the following problems from the textbook: p. 8 #1, 3, 4, and 7-23 odd. I may request that some of these be done on the board at the start of class next time.

For problems 7-23, where you need to approximate the limit graphically and numerically, you may want to try using Desmos as I did in class. There is also a Desmos app that you can use on your phone if you like. See the information on this page.

• Watch for the invitation to join the Piazza discussion board, which will be sent out over the next day or so to the email address that is listed for you in CUNYFirst. (Most likely it is your City Tech email address.)

Note also:
• Find and deal with your City Tech email: you must use this email address in WeBWorK and to join the Piazza discussion board. Also, City Tech is already sending you emails here!