11 SL Transformations of Trigonometric Functions

You should have the following questions completed by the end of class on Monday, April 8th. (In order to complete these, you may also find it helpful to read the textbook material in Sections B to F in the textbook.) Yes, there are lots of questions, but you’ve got lots of time!

One formula that you should have in your notes (this was discussed in our last class), is the formula to find the value of \(b\) that will change the period (of either \(f(x)=\sin (bx)\) or \(f(x)=\cos (bx)\)) to a desired value. That formula is given below.

\[b=\frac{2\pi}{\text{period}}\]

Questions
Exercise 10B.1 questions 1–4
Exercise 10B.2 questions 1–3, 4acegi
Exercise 10C questions 3–5
Exercise 10D questions 1adgi, 2, 3, 4
Exercise 10E questions 1–3
Exercise 10F questions 1, 2c, 3, 4ce, 4, 6ace, 7, 8

10 Philosophy Test

On Monday, April 8th we’ll have a test on the material we’ve covered so far (except the material on Plato that we’ve only just begun.)

The test will cover

  • The argument for existence given by Descartes
  • Logic (Truth tables and Validity, etc.)
  • Fallacies (What are they? What are the common types of fallacies?)

Your written task, your presentations (on the fallacies), and your logic quiz will be a good guide to the sorts of questions you will be asked. Make sure that you review both Google Docs on the fallacies.

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.