The3DCoordinateSystem
Well start the chapter off with a fairly short discussion introducing the 3-D coordinate system
and the conventions that well be using. We will also take a brief look at how the
Written Assignment Unit 3
University of People
MATH 1201: COLLEGE ALGEBRA
Instructions for submission
1. What are the least, and most, amount of distinct zeroes of a 7th degree polynomial, given that
NYC College of Technology, CUNY
Mathematics Department
Spring 2016
MAT 1475 Final Exam Review Problems
Revised by Prof. Kostadinov, Fall 2015, Fall 2014, Fall 2013, Fall 2012, Fall 2011, Fall 2010
Rev
Curvature
In this section we want to briefly discuss the curvature of a smooth curve (recall that for a
smooth curve we require
is continuous and
). The curvature measures how fast a curve is changing
CalculuswithVectorFunctions
In this section we need to talk briefly about limits, derivatives and integrals of vector functions.
As you will see, these behave in a fairly predictable manner. We will b
ArcLengthwithVectorFunctions
In this section well recast an old formula into terms of vector functions. We want to determine
the length of a vector function,
on the interval
.
We actually already know
Tangent,NormalandBinormalVectors
In this section we want to look at an application of derivatives for vector functions. Actually,
there are a couple of applications, but they all come back to needing
VectorFunctions
We first saw vector functions back when we were looking at the Equation of Lines. In that
section we talked about them because we wrote down the equation of a line in
in
terms of a vec
QuadricSurfaces
In the previous two sections weve looked at lines and planes in three dimensions (or
) and while these are used quite heavily at times in a Calculus class there are many other
surfaces
EquationsofPlanes
In the first section of this chapter we saw a couple of equations of planes. However, none of
those equations had three variables in them and were really extensions of graphs that we
FunctionsofSeveralVariables
In this section we want to go over some of the basic ideas about functions of more than one
variable.
First, remember that graphs of functions of two variables,
are surface
EquationsofLines
In this section we need to take a look at the equation of a line in
. As we saw in the
previous section the equation
does not describe a
line in
, instead it describes a plane. This d
Written Assignment Unit 4
University of People
MATH 1201: COLLEGE ALGEBRA
Instructions for submission
1.
If f(x) = 2x + 1 and g(x) = x2, what is f g? What is g f?
2. Consider f(x) = 2x + 3. Find the i