Spring 2008, Math 152 honors
Exam 2 Overview
Comment: It is assumed that you know integration techniques studied in 6.5, 8.1-8.3 and tested
in Exam 1. If unsure, review the material of these sections, too.
1. Chapter 8. (8.4, 8.8, 8.9). You need to know:
a) integration of rational functions by using partial fraction decomposition.
b) approximate integration: Left Point, Right point, Midpoint, Trapezoidal rule, Simpson’s rule. Be able to approximate an integral using an approximation formula and to estimate
an error made. You should be able to determine whether your approximation under- or overestimates the integral (for instance, knowing whether the integrand is increasing/decreasing
helps to decide for LP and RP; concavity up/down helps to decide for TR). Be able to
determine the smallest value of n needed for the desired error of approximation.
c) improper integrals of two types:
Definitions of improper integrals of type I and type II, evaluation of improper integrals when
exist.
Theorem, Limit Comparison Theorem. Know when improper integrals
R 1 1 Comparison
R∞ 1
dx,
dx,
are convergent/divergent since they are often used to compare with.
n
n
0 x
1 x
Suggested problems:
Page 508, 1, 17, 21
Page 519, 5-8, 23, 26, 28, 42, 44, 49, 51, 55, 58, 59, 60, 64, 67, 69, 71.
2. Chapter 9 (9.1-9.5).
a) Know definitions of: differential equation, order of a de, initial value problem, solution of
de, solution of ivp.
b) Be able to classify and to solve a separable differential equation (or a related initial value
problem).
b) Be able to classify and to solve a linear first order differential equation (or a related initial
value problem).
c) Know what a direction field is and be able to sketch a few directions for a certain equation.
Be able to recognize a direction field for a given equation if a few fields are given.
d) Be able to find an equation of a curve if its slope and a point on the curve are given.
e) Be able to set up and to solve an initial value problem for an application problem involving
rate of change (growth/decay, motion problems, salt in a tank, Newton’s law of cooling,
electric circuits, etc.)
f) Know how to compute the arc length for a given curve (cartesian, parametric, or polar).
g) Know how to compute the area of a surface of revolution.
h) Know how to find the moments and the centroid of a plane figure. Know Theorem of
Pappus.
Suggested problems: Page 570: 1-3, 5, 6, 7, 8, 9, 11, 12, 15, 16, 21, 24, 25, 26, 30, 32, 33