## 11 HL: The Definition of the Derivative

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

## 11 HL: Introduction to Derivatives

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 $$x=a$$?

## 11 HL: Limits at Infinity

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

## 11 HL: Limits and Continuity

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

## 11 HL: Introduction to Limits

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

Exercise 15A questions 1–5, 6abef

## 11 HL: Roots of Arbitrary Complex Numbers

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.

## 11 HL: Roots of Unity

Complete the questions in the file linked here. The second file here is more challenging (in parts), but you should try that one as well! There’s a hint for question 3 below.

Hint
For question 3, a proof by contradiction might be a good way to proceed!

## 11 HL: De Moivre’s Theorem

Complete the following questions before our next class.

Exercise 14F questions 2ce, 3bde, 4, 6, 8, 11

## 11 HL: Euler’s Form

Complete the following questions before our next class.

Exercise 14D.3 questions 4, 5, 7
Exercise 14E questions 1, 2, 4ab, 6ab

## 11 HL: Working with Modulus-Argument Form

Complete the following questions before our next class.

Exercise 14B question 13ac
Exercise 14C question 3