Kyle Smith Mike Scarpa Zack Orzech
In todays world there are many debates as to how humans were created and how
our world came to be the way it is. The main debate is whether it was created
through natural selection or intelligent design. Natural selectio
Math UN1201. Calculus III, Fall 2016, Section 001
Practice Midterm 1
Problem 1. (10%) Find the scalar and vector projections of h3, 4, 1i onto
h1, 1, 2i.
Problem 2. (10%) Classify the quadric surface x2 2z 2 + 6x y + 9 = 0.
(Your answer should be one of t
Mathematics UN1201. Calculus III, Fall 2016, Section 001
Practice Final Exam
1. Let P (2, 0, 5), Q(1, 2, 3), R(2, 3, 2) be three points in the threedimensional
space.
(a) Find an equation of the plane through P , Q, R.
(b) Find symmetric equations of the
Mathematics UN1201. Calculus III, Fall 2016, Section 001
Final Exam
Wednesday, December 21, 2016
9am12noon
Name :
UNI:
INSTRUCTIONS : There are 12 problems on this exam (total of 20 pages).
Please check that your copy contains all of the 20 pages and obt
Mathematics UN1201. Calculus III, Fall 2016, Section 001
Solutions to Midterm 1 (B)
Problem 1 (10%) Find the area of the triangle with vertices (1, 0, 2),
(5, 1, 1), (1, 1, 1).
Solution: The area of the triangle with vertices P (1, 0, 2), Q(5, 1, 1) and
R
Mathematics UN1201. Calculus III, Fall 2016, Section 001
Solutions to Midterm 1 (A)
Problem 1
(a) (8%) Find the scalar and vector projections of h1, 3i onto h2, 1i.
Solution: The scalar projection of b = h1, 3i onto a = h2, 1i is
compa b =
ab
h1, 3i h2, 1
Math V1201. Calculus III, Fall 2016, Section 001
Midterm 2
Wednesday, November 9, 2016, 8:409:55am
Name :
UNI:
INSTRUCTIONS : There are 6 problems on this midterm (total of 12 pages).
Please check that your copy contains all of the 12 pages and obtain a
Mathematics UN1201. Calculus III, Fall 2016, Section 001
Final Exam
Wednesday, December 21, 2016
9am12noon
Name :
UNI:
INSTRUCTIONS : There are 12 problems on this exam (total of 20 pages).
Please check that your copy contains all of the 20 pages and obt
EXAM 1 Review Questions
EXAM 1 REVIEW
Exams from last years Spring 2011, Fall 2012, Spring 2013, Fall 2013, Fall 2014 are posted on BB under EXAMS.
For the first exam you can study following questions from the following exams:
SPRING 2011: 1, 2a, 2b
Chap. 4.
Chemical Reactions
A chemical reaction is defined as the conversion of one set of substances called reactants into a
new set of substances named products.
A + B C + D
Carbon and oxygen react to produce carbon dioxide. Use chemical symbols and for
Math 202, Fall 2016  Exam 1 Template Questions are randomly selected.
On the exam you can see any kind of questions from past finals, WebWork
or textbook
Name:
Date:
Show ALL work. Do problems 1 and 2. Choose any TWO of the remaining problems.
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CC Study Guide Fall 2014 (Beau Shaw)
1.
Augustine City of God
(book 1:121; book 2: entire; book 12: 19.)
Background info: Augustine received a classical education rhetoric, Greek literature,
philosophy and politics. When he was only 30 years old he beca
Abnormal Behavior
Emett McCaskill, Ph.D.
Columbia University
Personality Disorders
Hooley et al (2016): Chapter 10
Personality
People differ from one another in
their intelligence, feelings, behavior, in
their view of themselves and others,
and in their
Name:
Instructor:
Shrenik Shah
MATH V1201, Section 12  Final
December 21, 2015 (170 minutes)
This examination booklet contains 9 problems, plus an extra credit problem. There are 13 sheets
of paper including the front cover and formula sheet at the back.
PRACTICE FINAL
CALCULUS III
(1)
Find the volume of the parallelopiped formed by:
u = h1, 0, 2i
v = h2, 1, 0i
w = h4, 1, 1i
Find the parametric equations describing the tangent line to the following parametric curve, at (2, 4, 3)
D
E
r (t) =
2t, 4 t3 , t
Calculus lll Practice Midterm Exam
October 7th, 2014
Write clearly and. Show all work.
This is a closed book test and no calculators are allowed.
Problem 1 5 pts. 
Problem 2 5 pts.
Problem 3 5 pts.

_
5pm 


_
Problem 5 5 pts.
Problem
Calculus lll Practice Midterm Exam
NOV 18th, 2015
Write clearlr and Show all work.
This is a closed book test and no calculators are allowed.
5pts _
spts. _
_5pts
_5pts.
5pts.
5pts. 
30 p138. Problem 1 (5 pts)
Find the equation of t
PRACTICE MIDTERM II
3
1) (20 pts) Find the length of the space curve r(t) = h t2 , t6 +
interval 1 t 2.
1
t
2t , 2 i
on the
2) (20 pts) Find x F (x, y) of y F (x, y) for
a) F (x, y) = ln(x2 + xy),
2
b)F (x, y) = ey +yx sin(x)
3) (20 pts) Find velocity and
Calculus III Practice Exam II
October 8th, 2015
NAME (please print):
UNI:
SCHOOL:
Write clearly and show all work.
This is a closed book test and no calculators are allowed.
Problem
Problem
Problem
Problem
Problem
Problem
Total
1
2
3
4
5
6
5 pts.
5 pts.
5
Calculus III Practice Exam I
Feb 17th, 2016
NAME (please print):
UNI:
SCHOOL:
Write clearly and show all work.
This is a closed book test and no calculators are allowed.
Problem
Problem
Problem
Problem
Problem
Problem
Total
1
2
3
4
5
6
5 pts.
5 pts.
5 pts
Homework 8
Due Monday, December 5, 2016 at the beginning of class.
REMEMBER TO WRITE DOWN YOUR OWN NAME AND THE FULL NAMES OF YOUR COLLABORATORS (for example: I worked with Kilroy Jenkins on problem 3 and Chauncey Whittelsey on
problem 7.)
Questions 1 and
Calculus I,
Columbia
University,
Fall 2013
Instructor:
Paul Siegel
Calculus I, Columbia University, Fall 2013
Instructor: Paul Siegel
September 23, 2013
Calculus I,
Columbia
University,
Fall 2013
What you should know
Instructor:
Paul Siegel
(or at least v
Problem: Show that lim x2 = 4.
x2
Let > 0. We want to find a > 0 such that if 0 < x 2 < , then
< . This choice of delta will in general depend on epsilon of course.
This is simply a game of inequalities. You want to make the first inequality
imply the s
CALCULUS I  PRACTICE EXAM 1
PAUL SIEGEL, INSTRUCTOR
Problem 1. Sketch the graph of the parabola y = x2 + 4x 1. Indicate the coordinates of the vertex on
your sketch.
Solution. We have:
x2 4x 1 = x2 4x 4 + 4 1 = (x + 2)2 + 3
Thus the graph of y = x2 + 4x
CALCULUS I  WRITTEN HOMEWORK 1  DUE 9/17/13
PAUL SIEGEL, INSTRUCTOR
Problem 1. Find the value of x in the diagram below which makes the large rectangle (with side lengths
x and x + 1) similar to the small rectangle (with side lengths 1 and x).
Problem 2
CALCULUS I  WRITTEN HOMEWORK 4  DUE 10/12/13
PAUL SIEGEL, INSTRUCTOR
Problem 1. For each of the following functions, find all horizontal and vertical asymptotes and use them
to sketch a graph.
x
(a) f (x) = 4x2 4x+1
(b) f (x) =
2x3 +16
x3 x
Problem 2. L