Week 2 Calculus I  Outline of Notes

by S. Gramlich

(updated 9/18/06)

 

 

1) 1.2, p. 26, Example 1 (see below)

            a) App B, p. A12, slope

            b) App B, p. A12, point-slope form

            c) App B, p. A13, slope intercept form

2) 1.2, p.29-35, types of functions & basic graphs

Algebraic:      polynomial (ldg coeff, degree/order, dv-int),

power [linear, quadratic, cubic, even, odd; root (odd/even index);

reciprocal (asymptotes)], rational;

Transcendental: exponential, logarithmic, trigonometric

3) Appendix D:  Trigonometry Review:

angles (rads/degrees),

terminal side,

6 trig fns,

identities,

ratios for certain angles (p.A27),

graphs (pp. A30-31 & pp. 33-34)

4) 1.1, [f(x+h) –f(x)] / h, p.23, #22

5) start 1.3, Graphing using Transformations/ Translations

 

 

 

 

 

Example 1

(from page 26, from "Calculus: Early Transcendentals,” 5th ed., by James Stewart, Brooks/Cole Publishing)

 

(a)  As dry air moves upward, it expands and cools.  If the ground temperature is 20 C and the temperature at a height of 1 km is 10 C, express the temperature (in C) as a function of the height h (in kilometers), assuming that a linear model is appropriate.

 

(b) Draw the graph of the function in part (a).  What does the slope represent?

 

(c) What is the temperature at a height of 2.5 km?