A quiz for practice on Sections 12.5, 12.6, 13.1, 13.2,
13.3
Covers HWKs 3-5, including the class problems from
13.1 & 13.2
Allow about 45 minutes
Questions as you prepare for the quiz? See me in office hours or send
me e-mail or post on the Q&A folder
in the FirstClass conference. To ask about a particular problem
from the text, give page or section number, give problem number,
and make your question as specific as you can. In the Q&A
conference, answer each other's questions as you can.
Suggestions for Practice Problems (don't do them all!):
12.5 p594: 1, 3, 11, 21, 22, 23
12.6 p598: some from 1-6, some from 7-11,
15, 17, 18, 19, 20, 21
What is meant by level surface for a function of 3
variables
How to find such level surfaces
Informal
definition for limit
Definition for a function being continuous
at a specified point
Finding limits using limit theorems and
continuity
Deciding where a given function is
continuous
Using the definition for continuity at a
point (for instance to decide whether a given function is
continuous at a given point, or to find values for a parameter
that will make a given function continuous)
Showing that a limit does not exist by
finding different paths that give different limits (text often
suggests which paths to use; quiz may not be quite so explicit
but paths of the kind used in the text should
suffice)
Working with sums, differences, scalar
multiples, and dot products of vectors (algebraically,
geometrically)
Verifying the equivalence of 2 definitions
(algebraic, geometric) for dot product
Using dot products to determine
length/magnitude of a vector, angle between vectors
In particular, deciding whether given
vectors are perpendicular, or finding a vector perpendicular to
a given vector
Deciding whether given vectors are
parallel, or finding a vector parallel to a given
vector
Finding the projection of one vector onto
another
Given some nonzero vector d,
resolving a vector v into a component parallel to
d and a component perpendicular to d
Given a point on a plane, and given a
normal vector for the plane, finding an equation for the
plane
Given an equation for a plane, finding a
normal vector for the plane
All of the notation and terminology listed
in the class handout for 13.1 & 13.2
Given equations for two planes, deciding
whether or not they are parallel
Given equations for two planes, deciding
whether or not they are perpendicular
Given a plane, finding inequalities
describing the two half-spaces into which the plane divides
3-space
Real-world interpretations/applications of
vectors, vector algebra, vector geometry
Using vectors in n-space, including finding
and interpreting sums, differences, scalar multiples, dot
products, magnitudes, angles (completely analogous to
the 2-space or 3-space calculations)