## 12 HL Taylor Series

Complete the following questions before our next class (these are from the Pearson book).

Pages 1411–1412 questions 17a, 23, 26abc

## 12 HL Power Series

Complete the following questions before our next class (these are from the Pearson book).

Page 1411 questions 1–16

## 12 HL Alternating Series

Complete the following questions before our next class.

Exercise K.3 questions 3, 4, and a few questions of your choosing from questions 7 and 9 (I suggest at least two from each).

## 12 HL The Ratio Test

Complete the following questions before our next class.

Use the ratio test to determine the convergence or divergence of the following series.

1. $\sum_{n=1}^\infty \frac{n^3 3^{n+1}}{4^n}$
2. $\sum_{n=1}^\infty \frac{n^{10}}{10^n}$
3. $\sum_{n=1}^\infty \frac{n^n}{n!}$
Click for a hint to question 3.
Consider the definition of $$e$$.

From the Haese book, complete Exercise K.3 question 1.

## 12 HL The Comparison Test(s)

Complete the following questions (from the Haese book) before tomorrow’s class.

Exercise K.1 questions 1acd, 3, 4bcef, 5

## 12 HL Sequences and Convergence

Complete the following questions before our next class.

(From the Haese book)
Exercise B.1 questions 3 and 5
(Read Section J, then complete )
Exercise J.1 questions 1bdf, 2acdf, 3
Exercise J.2 questions 1, 2, 3

Pay particular attention to questions 1 and 2 in J.2, which makes use of two (often useful) algebraic methods for showing that a sequence is monotonically increasing/decreasing: a sequence is decreasing if either $$u_{n+1}-u_n <0$$, or $$\frac{u_{n+1}}{u_n} <1$$ for all $$n$$, and with inequalities reversed either method establishes that the sequence is increasing.

## 12 HL Slope Fields and Euler’s Method

Complete the following questions before our next class.

(from the Haese book)
Exercise M questions 1, 5, 7, 8

(from the Pearson book)
pages 1467–1469 questions 14, 29, 30, 33

## 12 HL First-order Linear Differential Equations and Slope Fields

Complete the following questions before our next class.

(From the Haese book)
Exercise O (both questions 1 and 2)
Exercise M questions 3 and 6a

(From the Pearson book)
page 1467–1469 questions 5 and 17

## 12 HL Homogeneous Differential Equations

Complete the question we had started in class, and then complete the textbook questions listed below (all questions are from the Calculus Option chapter in the Pearson book).

$\text{Solve }\frac{dy}{dx}=\frac{x^2+3y^2}{xy}\text{, for }x,y>0.$

Complete p. 1470 questions 24, 25 and 27.

## 12 HL Separable Variables DEs

Complete the following questions (from Chapter 16 of the Pearson book) before next class.

Page 845 questions 1, 2, 6, 7, 13, 15, 17, 25, 28