MAT1475 – Calculus 1

WebWork

We will start using the online HW system WebWork going forward for most of our homework assignments. You should have received your WebWork login last week (on Tues Sept 10) via email. Here is the link for our section’s WebWork site again:

https://mathww.citytech.cuny.edu/webwork2/MAT1475-F24-Ganguli-D406

Your username is some variation of your “first initial+last name” and your password is your CityTech EmplID #. Please email me or talk to me in class if you can’t find your login info, or are having difficulties logging in.

The first WebWork set “Derivative – Limit Definition” is open, and is due next Monday (Sept 23). We did the first exercise in that set in class (see below).

Topics/Boardshots

We continued with the “limit definition of the derivative” f'(a), and introduced the idea of “the derivative as a function”, i.e., f'(x). We also did an example from the WebWork:

Starting with the numerical calculations in Example/Checkpoint 2.1 (Sec 2.1), we reviewed slopes of secant lines and the definition of the derivative, and used it to calculate f'(1) for f(x) = x^2:

The definition of the derivative is covered in Sec 3.1 of the textbook. Please read the start of that section, including Figures 3.3 and 3.4, which is another presentation of the figures you were asked to draw for HW#1:

Reminder – HW#1 & Quiz #1 Wednesday:

HW#1 will be due Wednesday (Sept 11). Please write out the solutions to the following exercises from the OpenStax textbook on paper and hand them in on Wednesday. Also we will take a short quiz at the end of class Wednesday, with one or two exercises similar to the HW exercises. This quiz will be open book–you can use your HW and class notes.

We went through the concepts and techniques for the exercises in HW#1:

• simplifying f(a+h) for a given function f(x) — with the followup of simplifying f(a+h) – f(a), and then [f(a+h) – f(a)]/h, for the definition of the derivative!
• equations of lines, in particular the point-slope form (since this is what we will use to write down equations of tangent lines
• finding slopes of secant lines