Things that will definitely appear on final exam:

log-log plots (but no semi-log plots) -- see log-log problems plus answers

Ch 8:

Note: you should be able to recognize standard functions, including lines, t^2, t^3, exponential growth, exponential decay, ln, sin, cosine.

Review 8.1, 8.3, 8.4 HW
Review TF (including multiple choice slope fields problems)

Note: For sections 8.2, 8.5 you only need to know/understand TF problems.

Generic Review (i.e. some of the following will appear on your exam and some will not.)

Ch 5:

Fully understand integration:

1.) Definition
Be able to approximate the integral using inscribed or circumscribed rectangles – see class notes, HW problems 5.2: 1- 2 or better examples here
2.) Can be used to find actual area, net area, volume - see HW in sections 5.2, 5.3, 5.8, exam 2, quizzes, and class notes.
Also see 5.9: Improper integral -- See class notes and 5.9 HW.

Be able to calculate integrals
-- integration by substitution -- 5.5 HW
-- integration by formula -- 5.7 HW
-- you do not need to know integration by parts

Not on final exam: section 5.6

Ch 4:

Understand exponential decay/growth. Compare 8.4 to 4.3 and 4.4
Know log rules
Log-log plots
Also see below

Not on final exam: semi-log plots

Ch 3:

Fully understand how the derivative (first and second) applies to graphing

3.5: Optimization – Very important application
--Understand relative vs absolute max/min
--Understand Extreme Value Theorem
See 3.5 HW as well as min/max problems in other sections including Ch 4

3.6: Understand that the tangent line to y = f(x) at the point (a, f(a)) is a good approximation to the function y = f(x).
That is if the tangent line to y = f(x) at the point (a, f(a)) is the function y = mx + b, then f(x) ~ mx + b for x close to a. Thus

1.) You can use the tangent line to approximate the function y = f(x). See for example HW problems 3.6: 11 – 20. Make sure that you FULLY understand these problems.

2.) You can also use the tangent line to approximate solutions to the equation f(x) = 0. By doing multiple rounds of Newtons method, you can get a very good approximation. However, you only need to do at most one round. See lecture notes from 12/5 (a) find tangent line (y = mx + b) at appropriate point (b) since f(x) ~ mx + b, instead of solving f(x) = 0, solve mx + b = 0

Note you only use Newton’s method IF asked to solve f(x) = 0

FYI (i.e. not on exam): in real applications, to solve f(x) = k, instead solve f(x) – k = 0.

3.7: Implicit differentiation and related rates – Very important application. See HW, class notes, and this week's double quiz.

Ch 2:

Fully understand the derivative
--slope of tangent line
--instantaneous rate of change vs average rate of change
--limit definition

Be able to calculate the derivative. Practice problems from ch 2, 3 and 4 as well as exams.

Understand and be able to calculate limits: see 2.1, 2.2 and ch 4

Ch 1:

Pre-calculus is assumed. Know sin and cosine values.