Week 2 Calculus I
Outline of Notes
by
(updated
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?