Attached is a set of questions that you can use to practice the chain rule. We can look at the answers in our lesson tomorrow.
Welcome Back!
Welcome back for Year 13, and our second year of Mathematics HL!
This year we’ll be in Mathematics 12, in the Mathematics Corridor (formerly the English Corridor—our room was formerly Ms Donnelly’s room), and our first lesson will be Sunday, Lesson 5.
Ready?
Operations with Taylor Series
From Chapter 30 of the Cambridge book, complete the following questions for Wednesday this week.
page 5 question 5,
page 11 questions 4 and 5,
page 14 question 2 a),
page 15 question 9,
page 19 question 8.
Fun with Comparison Tests
Your challenge tonight is to come up with a series that can be shown to converge using (either version of) the comparison test. We’ll vote on the best example tomorrow. Here’s my entry.
\[\sum_{n=1}^\infty \frac{1}{2^n-n^2}\]
Calculus (Option Topics) Test 1 [Updated]
We’ll have our first test on the Calculus Option topics on Sunday, March 6th.
This test will cover material that includes differential equations, important theorems and definitions in Calculus (Rolle’s Theorem, the Mean Value Theorem, continuity and differentiability, etc.), and l’Hôpital’s Rule.
Update: The following questions will be useful.
page 1471–1474 questions 1, 4, 10, 16, 19, 22–27
page 1436 questions 9, 17
page 1354 questions 4, 6, 14, 15
Euler’s Method Homework Assignment
Complete the questions on this PDF file for the beginning of class on Wednesday, March 2nd.
Euler’s Method [Updated]
You should now have received an email with a list of questions. Complete questions 4, 7, and 14 for tomorrow’s class.
Update: note that there’s an error in question 14: \(y(2)\), rather than \(y(3)\), should appear in part c).
Homogeneous Differential Equations
Complete page 1470 questions 25 and 27. You will find it helpful to simplify expressions as much as possible in your intermediate steps.
The Mean Value Theorem
While I’m sure you’ve all written down these questions, you should complete p.1436 questions 7, 10–13, 15 for tomorrow’s lesson.