Mathematics for social sciences (multivariable calculus)
MATH 19520

Fall 2016
Math 195 Section 51 Practice Midterm 1
October 22, 2015
Answer the questions in the blue book to the best of your ability. Show your work.
1. For this question, c is a scalar, P is a point, and ~u, ~v are vectors.
Write three operations that make sense us
Mathematics for social sciences (multivariable calculus)
MATH 19520

Spring 2010
CLASS QUIZ: APRIL 8: VECTORS
MATH 195, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
A (*) in front of a question indicates that there exist one or more strong distractors in the answer choices,
so you need to be more careful.
(1)
Mathematics for social sciences (multivariable calculus)
MATH 19520

Spring 2010
CLASS QUIZ: APRIL 27: MULTIVARIABLE FUNCTION BASICS
MATH 195, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
(1) Suppose f is a function of two variables, dened on all of R2 , with the property that f (x, y ) = f (y, x)
for all real
Mathematics for social sciences (multivariable calculus)
MATH 19520

Spring 2010
CLASS QUIZ: MAY 23: MAXMIN VALUES: TWOVARIABLE VERSION
MATH 195, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
(1) Suppose F (x, y ) := f (x) + g (y ), i.e., F is additively separable. Suppose f and g are dierentiable
functions o
Mathematics for social sciences (multivariable calculus)
MATH 19520

Spring 2010
CLASS QUIZ: MAY 13: MULTIVARIABLE INTEGRATION
MATH 195, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
The following setup is for the rst ve questions only.
Suppose F is a function of two real variables, say x and t, so F (x, t) is
Mathematics for social sciences (multivariable calculus)
MATH 19520

Spring 2010
CLASS QUIZ: MAY 2: PARTIAL DERIVATIVES
MATH 195, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
(1) Consider a production function f (L, K, T ) of three inputs L (labor expenditure), K (capital expenditure), and T (technology expend
Mathematics for social sciences (multivariable calculus)
MATH 19520

Spring 2010
CLASS QUIZ: APRIL 29: MULTIVARIABLE LIMIT COMPUTATIONS
MATH 195, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
(1) Consider the function f (x, y ) := x sin(1/(x2 + y 2 ), dened on all points other than the point (0, 0).
What is the
Math 195, Section 55
Instructor: Chris Skalit
First Hour Exam
You have 50 minutes to complete the exam. The use of calculators, cellphones, notebooks,
etc. is strictly prohibited. Partial credit will be awarded for answers that are either incomplete or sl
Math 195, Section 55
Instructor: Chris Skalit
Quiz 7
Name:
1. Consider the function, f (x, y ) = x(y 2 1) dened on the domain, D = cfw_(x, y )x2 + y 2 4, y 0
(pictured below). Compute the absolute maximum and minimum achieved by f on D.
y
y=
4 x2
x
2. A
Math 195, Section 55
Instructor: Chris Skalit
Quiz 1
Name:
1. Consider the parametricallydened curve, given by the equations, x = t2 and y =
(a) (1 point) Compute
t3
+6.
3
dx
dy
and
.
dt
dt
Solution:
dx
= 2t
dt
dy
= t2
dt
(b) (2 points) What is the equat
Mathematics for social sciences (multivariable calculus)
MATH 19520

Spring 2010
CLASS QUIZ: MARCH 30: PARAMETRIC STUFF
MATH 195, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
A (*) in front of a question indicates that there exist one or more strong distractors in the answer choices,
so you need to be more car
Mathematics for social sciences (multivariable calculus)
MATH 19520

Spring 2010
CLASS QUIZ: APRIL 1: POLAR COORDINATES
MATH 195, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
A (*) in front of a question indicates that there exist one or more strong distractors in the answer choices,
so you need to be more car
Mathematics for social sciences (multivariable calculus)
MATH 19520

Spring 2010
CLASS QUIZ: APRIL 6: THREE DIMENSIONS
MATH 195, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
A (*) in front of a question indicates that there exist one or more strong distractors in the answer choices,
so you need to be more care
Mathematics for social sciences (multivariable calculus)
MATH 19520

Fall 2016
Math 195 Section 51 Practice Midterm 2
November 13, 2015
Answer the questions in the blue book to the best of your ability. Show your work.
1. Give the definition for the following:
lim
f (x, y) = L
(1)
(x,y)(0,0)
2. Define f (x, y) as follows:
f (x, y) =
Mathematics for social sciences (multivariable calculus)
MATH 19520

Fall 2016
Math 195 Section 51 Midterm 1
December 8, 2015
Answer the questions in the blue book to the best of your ability. Show your work.
1. Which of the following make sense? Further, which kind of object (point, scalar, vector) is each?
For this question, c, d
Mathematics for social sciences (multivariable calculus)
MATH 19520

Fall 2016
Math 195 Section 51 Practice Final Exam
December 9, 2015
Answer the questions in the blue book to the best of your ability. Show your work.
1. Find the following:
(a) h1, 1, 3i h9, 4, 2i
(b) h6, 1, 4i h2, 7, 5i
(c) f , where f (x, y, z) = sin4 (xy + yz +
Mathematics for social sciences (multivariable calculus)
MATH 19520

Fall 2016
Math 195 Section 51 Midterm 2
December 9, 2015
Answer the questions in the blue book to the best of your ability. Show your work.
1. Give the definition for the following:
f~(x, y) = ~r
lim
(x,y)(0,0)
2. Define f (x, y) as follows:
f (x, y) =
0
1
: x2 < y
Mathematics for social sciences (multivariable calculus)
MATH 19520

Spring 2010
Homework 4
Math 19520 (section 43), Fall 2016
This homework is due in class on Wednesday, October 26th. You may cite results from class as appropriate. Unless otherwise stated, you must provide a complete explanation for your solutions, not simply an
answ
Mathematics for social sciences (multivariable calculus)
MATH 19520

Spring 2010
Homework 3
Math 19520 (section 43), Fall 2016
This homework is due in class on Wednesday, October 19th. You may cite results from class as appropriate. Unless otherwise stated, you must provide a complete explanation for your solutions, not simply an
answ
Mathematics for social sciences (multivariable calculus)
MATH 19520

Spring 2010
Homework 2
Math 19520 (section 43), Fall 2016
This homework is due in class on Wednesday, October 12th. You may cite results from class as appropriate. Unless otherwise stated, you must provide a complete explanation for your solutions, not simply an
answ
Mathematics for social sciences (multivariable calculus)
MATH 19520

Spring 2010
Homework 1
Math 19520 (section 43), Fall 2016
This homework is due in class on Wednesday, October 5th. You may cite results from class as appropriate. Unless otherwise stated, you must provide a complete explanation for your solutions, not simply an
answe
Mathematics for social sciences (multivariable calculus)
MATH 19520

Spring 2010
CLASS QUIZ: MARCH 28: PARAMETRIC STUFF
MATH 195, SECTION 59 (VIPUL NAIK)
Your name (print clearly in capital letters):
(1) Consider the curve given by the parametric description x = cos t, y = sin t, where t varies over the
interval [a, b] with a < b. Wha
Math 195, Section 55
Instructor: Chris Skalit
Practice Problems for Chapter 15
Name:
sin(2x y ) dA where D = [0, ] [, ].
1. Compute
D
Solution: A straightforward application of Fubinis Theorem gives
sin(2x y ) dy dx
sin(2x y ) dA =
0
D
sin(2x y ) dy and r
Math 195, Section 55
Instructor: Chris Skalit
Second Hour Exam
You have 50 minutes to complete the exam. The use of calculators, cellphones, notebooks,
etc. is strictly prohibited. Partial credit will be awarded for answers that are either incomplete or s
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by Ca
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com
Generated by CamScanner from intsig.com