Name: 1 (20 points). Estimate the double integral
R
cos(y/x) dA, where R is the rectangle [0, 2][0, /2]
using a double Riemann sum with four sub-rectangles. Use the upper right corner of each subrectangle for the sample point.
It's probably best to draw t
MATH 2008A w Intermediate Calculus w Fall 2013
Test 2
Date: 23 October 20:33 ':£é:35m-:1?:25
Instructmr: Flof. L. Campbeii
NAME: , . 133% W
This exam has 4 questions (for a total of 22 lnarks). Answer 311 4 questions.
N0 calculators allowed.
1. Show tha
Math 2008 Midterm 1 Duration: 50 Min
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Signature:
Student ID numb er:
fgvlv‘lmllﬁw
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Special Instructions: No books OR notes are allowed. You may use a basic calculator. All electronic devices
must be turned off (especially. cel
Math 2008, Midterm 3 Duration: 50 Min
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Signature:
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Special Instructions: No books OR notes are allowed. You may use a basic calculator. All electronic devices
must be turned off (especially cell phones). Pleas
Math 2008, Midterm 4 Duration: 50 Min
Name (please print): a-
Signature:
Student ID number:
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Special Instructions: No books OR notes are allowed. You may use a basic calculator. All electronic devices
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Math 2008, Midterm 2 Duration: 50 Min
Name (please print):
Signature:
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Special Instructions: No books OR, notes are allowed. You may use a basic calculator. All electronic devices
must be turned off (especially cell phones). Pl
MATH 2004/2008 Summer 2014
Sample Mid-term Test - 30 Marks
1. [4 marks] The directional
of a differentiable
function f (x, y) at the point (a, b) in
derivative
the directions (1/ 2, 1/ 2) and (1/ 2, 1/ 2) equals 3 and 2, respectively. Find the
largest c
MATH 2004/2008 Summer 2014
Assignment 1 - Due: Thursday, July 17th at the beginning of tutorial.
1. Let f : R2 R be given by f (x, y) = exy sin(y), for (x, y) R2 . Verify that f satisfies Clairauts
Theorem, i.e., show that fxy = fyx .
2. Consider the func
MATH 2004/2008 Summer 2014
Tutorial 2 - Thursday, July 17th .
1. Find the points on the sphere x2 + y 2 + z 2 = 4 that are closest to and farthest from the point
(3, 1, 1). [Hint: Minimize/maximize the squared distance.]
Solution: The distance from a poin
MATH 2008/2009 A Test 1
Thursday, September 30th, 2010
This test has 3 questions (worth a total of 15 marks). Calculators are
not allowed. You have 50 minutes. Put a box around your nal answers.
1. (5 points)
(a) Find a unit vector in the same direction a
MATH 2008/2009 A Test 2
Thursday, October 14th, 2010
This test has 4 questions (worth a total of 15 marks). Calculators are
not allowed. You have 50 minutes. Put a box around your nal answers.
1. (3 points)
Show that
2xy 2
does not exist.
(x,y )(0,0) x4 +
MATH 2008/2009 A Test 3
Thursday, November 4th, 2010
This test has 5 questions (worth a total of 15 marks). Calculators are
not allowed. You have 50 minutes. Put a box around your nal answers.
1. (3 points)
Find the directional derivative of f (x, y ) = x
MATH 2008/2009 A Test 4
Thursday, November 18th, 2010
This test has 3 questions (worth a total of 15 marks). Calculators are
not allowed. You have 50 minutes. Put a box around your nal answers.
1. (6 points)
Find the volume of the solid enclosed by the pa
MATH 200813 Intermediate Calculus « Fall 2014 A
Test 1
Date: 4 February 2014; 19:3520:25
Instructor: Prof. E. Lorin
NAMES) V
ID#: (DOD-C) 75,11
This exam has 4 questions (total 25 marks). Answer all 4 questions.
Documents and calculators are not allo
MATH 2008B Intermediate Calculus Fall 2014 I 5:)
Test 2 '
Date: 4 March 2014; 19:3520:25
Instructor: Prof. E. Lorin
ID#: M20959 1,15 :3-
This exam has 4 questions (total 25 marks). Answer all 4 questions.
Documents and calculators are not allowed.
. 1"!
MATH 2004/2008 Summer 2014
Assignment 1 - Due: Thursday, July 17th at the beginning of tutorial.
1. Let f : R2 R be given by f (x, y) = exy sin(y), for (x, y) R2 . Verify that f satisfies Clairauts
Theorem, i.e., show that fxy = fyx .
Solution: [4 marks]