Monday 10 February class

Topics:

• Careful use of = signs in doing computation of difference quotient (or anything else): more similar usage comments are below.

• Using the graphing calculator: see the handouts for topics. In this context we encountered Wheeler’s first moral principle: never solve a problem until you know the answer. (We saw that you need to know more or less what the graph looks like in order to be able to interpret what the graphing calculator was showing. But the principle is generally useful.)

• The square root principle: see below

Usage comments:

• Don’t use arrows in place of equals signs. The double arrow is used between statements (for example, two equations) and it means “if the first one is true, the second one is also true”. You should avoid using it unless absolutely necessary: instead, put each successive equation on a separate line.

• In general, leave a lot of space in your work. It makes it easier to read and understand, and it makes it easier to make corrections!

• When solving an equation of the form (something), we use the Square Root Principle:

If , then

$latex x = \pm\sqrt{c}

Note: there is no “missing step”. We do not “take the square root of both sides”. What is wrong with doing that has to do with the fact that is NOT necessarily x. (And yes, I know that some teachers tell you to “square root both sides”, ugh, but it is still wrong, and will cause you trouble later on.)

Here is a video that explains it correctly. (You’ll have to sit through an annoying ad first, but the video is good and is totally mathematically correct.)

If you write the incorrect version, it is an error (that’s the main consideration!) and will cause you to have fewer points on that problem (if that’s all you care about). So correct this in your thinking if necessary!

Homework:

• Review the examples discussed in class. Especially make sure that you understand the usage notes above, and the square root principle. Practice on the examples in the textbook, making sure that the things on each side of an = sign are actually equal to each other.

• Practice practice practice with your calculator, remembering to examine your results against what else you know as a check

• Do the assigned exercises from Session 4

• Do the WeBWorK assignment (due by Tuesday the 18th 11 PM) – start early!

• Join Piazza (if you have not already done so) and join the MW group in Piazza – and use it if you have any questions about the homework problems! If you responded to the first Warm_Up (Exercise 1.1) you should have received an email inviting you to join the Piazza for this course

• Do the Warm-Up in Piazza (also due by Tuesday the 18th 11 PM)