Math 006 - Introduction to Calculus

Lecture 8

New Stuff

We will cover the following topics in this class:

• Trigonometric functions Explaination of what trigonometric functions are, with examples and applications, and their graphs. Some trigonometric identities. Some trigonometric equations.

Before starting on trigonometric functions, we will finish the idea of curve sketching, going over sections 5.4 and 5.5 of the text book. Then we will cover the review section of chapter 6, and start on section 6.1.

Curve sketching

We have covered all the points we need to use for curve sketching, in week 6 and week 7 we just need to put them together. We will follow the list given on pages 233 and 234 of the text book. This is section 5.5 of the text book, and several examples can be found there. A further example can be found on the quiz page.

Tutorial and Examples

The following questions from the text book should be done for practice, but are not to be handed in for marking.

• Ex 5.5 Page 240, B Ex 1, 3, 5, 9
• Ex 1, page 252, 1.a,f; 2.a,f, 3,4
• Please read the review section to chapter 6

Answers to the following questions should be handed in Wednesday 25 March.

For the functions below, find all of the following, and sketch the graph of the function:

(i) Domain

(ii) Intercepts

(iii) Asymptotes

(iv) Intervals of increase / decrease

(v) Local maximum and minimum

(vi) Concavity, convextity, points of inflection (not in case D)

A. (x² - 4)³

B. (x² - 4)^1/2

C. (x - 1)/(x + 1)²

D. 1/(x(x + 2))

Sample Quiz

There will be a quiz next week, which will be similar to the following question:

Find the intercepts, asymptotes, local max and min, of the function (x² - 5)/(x -3), and use this to sketch the graph on the interval [-6,6]. (grid will be provided)

Handout

Please send corrections to spelling mistakes, and any other comments, to me.