Mathematics 134 -- Intensive Calculus for Science 2
Quiz 2
January 30, 2002
The second regular quiz of the semester will be given during
the first 20 minutes of class on
Friday, February. It will cover the material from sections
6.1 - 5.3 that we have discussed since the start of the
week. No calculators on this quiz. The specific topics
to be covered will be:
- The ``eternal gem'': The Fundamental Theorem of Calculus.
If f is continuous on a <= x <= b and
F is an antiderivative of f, then
intab f(x) dx = F(b) - F(a)
Know this statement and how it comes by thinking of the
integral of f as computing a total change in F.
- Antiderivatives graphically and numerically. Given a graph
of f(x) for a <= x <= b, be able to generate a
sketch of the graph y = F(x) where F'(x) = f(x),
and F(a) = given. I will give you enough information
to be able to determine values of F for at least some
x -- for instance by using the Fundamental Theorem and
facts about areas between the graph of f and the x-axis.
- Antiderivatives (indefinite integrals)
for f defined by formulas -- know how to find
antiderivatives for powers,
exponentials, sin, cos, and sums and constant multiples of these.
- Using the Fundamental Theorem to compute definite integrals.
- First examples of differential equations. Finding an indefinite
integral for f is the same as solving the differential equation
dy/dx = f(x) for y. The arbitrary constant can
be chosen to satisfy an initial condition y(a) = y0.
-
On the quiz, there will be three
questions similar to problems from this week's problem assignment.
Good Review Problems
Chapter 6, Section 1: 1, 3, 17
From Review Problems for Chapter 6 (page ): 1-10
Chapter 6, Section 2: 75, 81
Chapter 6, Section 3: 1, 9