Math 126 Spring 2010
Work with projections, dot products, and cross-products.
1. Decide for each expression below whether it is a vector (V), a scalar (S), or nonsense (N).
Note that a, b, u, and v are vectors, while c and d are scalars.
Circle one:
(a)
a
Math 126
Optimization
Recall: The critical points of f (x, y) are points (x0 , y0 ) in the domain of f such that:
fx (x0 , y0 ) and fy (x0 , y0 ) are BOTH equal to 0; OR
at least one of fx (x0 , y0 ) or fy (x0 , y0 ) is undefined.
The Second Derivative
Math 126, Section C, Autumn 2012, Midterm I
October 18, 2012
Name
TA/Section
Instructions.
There are 4 questions. The exam is out of 40 points.
You are allowed to use one page of notes written only on one side of the sheet in your own handwriting.
Hand
Worksheet 3 Solutions
1. Surfaces: For the surface x + y 2 z 2 = 4.
If x = k is xed, then the traces are hyperbolas.
If y = k is xed, then the traces are parabolas.
If z = k is xed, then the traces are parabolas.
This shape is called a hyperbolic para
Worksheet 3: Surfaces, Parametric Facts, and Polar Facts
This worksheet reviews and summarizes several topics that you are learning right now (or are about to
learn). The front should be mostly review and the back introduces polar coordinates. Use this ti
Worksheet 1: Calculus Review Answers and Solutions
1. Derivatives
(a) See my review of calculus 1on how to do these or talk to a tutor. Here are the answers:
7
6
a) y = 50x9
b) y = 154 x
c) y = 6x sin(3x2 ) d) y = x + x2
5
2
e) y = (5x)2 +1 f) y = 6 sec(2
Worksheet 1: Calculus Review
On a separate sheet of paper, attempt the following problems. At the end of class turn this in with your
name on top and you will get participation points (as long as you attempted at least half the problems).
There is no pres
Worksheet 2c: Correctly Parameterizing a Line
Story: You are watching Gary Potter on his magical ying broom. You impose a coordinate system so
that the ground is the xy-plane. At precisely noon, the back of the broom is at the point P(1,2,22) and
the fron
Math 126 Autumn 2009
Work with lines and planes.
1. Decide by yourself whether each of the following is true or false. Compare answers with one
or two neighbors, then conrm your answers by using pieces of paper and/or a desktop as
models for planes, and p
MATH 126 LECTURE EXAMPLES
1. Your current grade in this course is given by a two-variable function G(h, m), where
h is your homework percentage and m is your first midterm score out of 50 points.
Possible values of G are given in the table below. (NOTE: I