Author: Dr. McDonald

Complete the following questions before our next class.

Exercise 17C questions 2, 3, 4, 6, 8

Complete the following questions before our next class.

Exercise 17B.1 question 2
Exercise 17B.2 questions 3, 4, 5, 6, 7

Complete the following questions before the start of class on Tuesday, August 25th.

Complete:

• Review Set 16A (all questions)
  For question 6 you can use the rule that \[\textrm{If } f(x)=x^n, n\neq 0, n\in \mathbb{R}\textrm{, then }f'(x)=nx^{n-1}\] rather than using first principles. (Also, remember that “from first principles” is the way that some textbooks will indicate that they want you to start from the definition.)
• Exercise 17A questions 2, 3, 6, 7cdef, 8, 11

(If you finish this and want to work ahead, continue reading Chapter 17.)

Complete the following questions (and any others you haven’t finished) before class on Tuesday.

Exercise 16A.1 question 2
Exercise 16A.2 questions 1 and 3 (read, but don’t complete, question 4)
Exercise 16C question 3ab
Exercise 16D question 3
Exercise 16E questions 2 and 7

Using the method presented in class, calculate the derivative of \(f(x)=x^2\) at the point \(x = 5\).

Bonus (as suggested by Amin): Using that same method, can you find an expression equal to the derivative of \(f(x)=x^2\) at the point \(x=a\)?

Complete the following questions before our next class. Before completing these questions, make sure you read section 15C in the textbook.

Exercise 15C questions 2ade, 4, 5

Complete the following questions before our next class. You’ll find it helpful to read textbook sections 15B and 15E.

Exercise 15B questions 2, 4, 5, 6, 8
Exercise 15E questions 1, 2, 4abde, 5a

Read sections 15A (along with the example) and complete the following questions before our next class.

Exercise 15A questions 1–5, 6abef

Here I’ve attached the entire PDF presentation from today’s class. I suggest you read through that presentation and complete the questions on page 5 and 6 (page 5 contains the questions you’ve already worked on in class, so those may already be finished!).

If you want to finish complex numbers completely, read the final two slides, and give the questions from the textbook a try. (This would be a great way to review your understanding of complex numbers before the end-of-year exam!)

Update: Here’s a GeoGebra applet that will let you view the roots of an arbitrary complex number.