ENGR0135  Statics and Mechanics of Materials 1 (2141)
Homework #1
Due: 9/4(daytime sections) or 9/3(evening section)
1. Two spherical bodies weigh 500 lb and 1500 lb at the Earths surface. Determine the
gravitational force of attraction between the spher
Math 240 Analytical Geometry and Calculus III Practice Final Exam April 24, 2006 Name (Print): Circle the name of your instructor: Dimitric Athanas Hales
Instructions: 1. Show all your work on the exam itself; use backs of the pages if necessary. Provide
MATH 0240 Final Sample Exam 6
Problem 1. Find the points on the cone z 2 = x2 + y 2 closest to the point
(1, 3, 4).
Problem 2. Express the volume of the tetrahedron with vertices at
points (0, 0, 0), (1, 0, 0), (0, 2, 0), (0, 0, 3) as a triple integral. W
MATH 0240 Final Examination Sample 6  ANSWERS
Problem 1. ( 3 , 3 2 3 , 3)
2
Problem 2. There are 6 possible correct answers. One of the possible
answers is:
y
z
1 (22x) (1 2 3 )
dz dy dx
0
0
0
Problem 3. There are innitely many possible answers. An examp
MATH 0240 Midterm Examination I Sample 2
This test consists of 10 problems. All work must be shown in order to
get credit. Please write legibly and explain your logic by words whenever
appropriate. If more space is needed, write on the back of the pages a
MATH 0240 Midterm Examination I Sample 2  ANSWERS
Problem 1.
2
Problem 2. 10x + 3y = 16
Problem 3. a) (0, 0), (0, 2), and (1/2, 2)
b) All three points are saddles.
Problem 4. Maximum:
Problem 5.
f
x
y
97; Direction: < 9, 4 >
x
= y e +ze x and
cos z+e
f
y
MATH 0240 Midterm Examination I Sample 3
This test consists of 10 problems. All work must be shown in order to
get credit. Please write legibly and explain your logic by words whenever
appropriate. If more space is needed, write on the back of the pages a
MATH 0240 Midterm Examination I Sample 1  ANSWERS
Problem 1.
2
3
Problem 2.
4
3
Problem 3. 4 2
Problem 4. (2, 1, 1) and (4, 4, 8)
2
Problem 5. < 1 , 2 , 3 >
3 3
Problem 6.
3
2 2
Problem 7. L(x, y) = 3 + (x 1) + 2y
Problem 8.
Problem 9.
1
2
1
and 2
x
1
x
MATH 0240 Midterm Examination I Sample 1
This test consists of 11 problems. All work must be shown in order to
get credit. Please write legibly and explain your logic by words whenever
appropriate. If more space is needed, write on the back of the pages a
Name: “*im‘ii

MATH 240 — Midterm I
Instructor: Hisham Sati
Monday October 6, 2014
_ This midterm contains 5 problems of equal weight.
Do all of your work on the sheets, and show all your computations.
This is a closed book exam.
The use of calculators
Exam 1 Review:
You should not assume that the rst midterm exam will resemble this review sheet. The
problems below were chosen because they seemed interesting or because they illustrated an
important concept. They are not meant to be typical exam problems
Exam 1 Review:
You should not assume that the rst midterm exam will resemble this review sheet. The
problems below were chosen because they seemed interesting or because they illustrated an
important concept. They are not meant to be typical exam problems
MATH 0240 Final Examination Sample 5  ANSWERS
Problem 1. (1): x + y z = 1;
(2): 23 .
Problem 2. w = fx sin cos + fy sin sin + fz cos
w
= fx cos cos + fy cos sin fz sin
w
= fx sin sin + fy sin cos
Problem 3. 1; 1; x + y + z = 3
Problem 4. (1, 0) and
MATH 0240 Final Examination Sample 7  ANSWERS
Problem 1.
2 6
3
Problem 2. Abs. min at (0, 0), (1, 0) and (0, 1) (value 0);
1
2
Abs. max at ( 3 , 2 ) (value 33 )
3
Problem 3. a) < 0, 2, 3 >
b) 0, 2, 3 >
<
c) 5
d) x = t, y = 1 + 2t, z = 1 + 3t.
1
Problem 4
MATH 0240 Final Examination Sample 8  ANSWERS
Problem 1. x = 1 + 3t, y = 2 t, z = 3 2t
Problem 2.
56
.
6 6
Problem 3. a)
44
;
5
b)
89; c) z = 8x + 5y 11.
Problem 4. (2, 3) and (2, 3)  both saddles.
Problem 5. 1
3
Problem 6. 40
Problem 7. a) yes; b) ln
MATH 0240 Midterm Examination II Sample 1  ANSWERS
20
Problem 1. 8 , 49 .
7
Problem 2.
4
.
15
Problem 3. 10.
Problem 4.
Conservative; f (x, y) = xy 2 cos(2x) (you can add any constant)
Problem 5.
1y 2
1
(x2 + 5y)dxdy
0
1y
Problem 6. u2 v 2 w2 + 2uvw 1
MATH 0240 Midterm Examination II Sample 2
This test consists of 11 problems. All work must be shown in order to
get credit. Please write legibly and explain your logic by words whenever
appropriate. If more space is needed, write on the back of the pages
MATH 0240 Midterm Examination I Sample 3  ANSWERS
3
Problem 1. < e 1, 0, 3 >
3
Problem 2. < t, t6 + t, 1 >
Problem 3. 0 and
3
2
Problem 4. z 75 = 32(x 4) + 48(y 2)
Problem 5. 2/5
Problem 6. 60x2 y 3
Problem 7. (0, 0); it is a saddle
Problem 8. 65
Problem
MATH 0240 Midterm Examination II Sample 3
This test consists of 10 problems. All work must be shown in order to
get credit. Please write legibly and explain your logic by words whenever
appropriate. If more space is needed, write on the back of the pages
MATH 0240 Midterm Examination II Sample 3  ANSWERS
Problem 1. 1 f t 1 f t 3/2 f t.
Problem 2.xy + yz ln(x2 + z 2 )
Problem 3. a) maximum: 7; minimum: 5
b) 1
Problem 4.
1cos(27)
3
Problem 5. (0, 1 )
2
Problem 6.
.
2
Problem 7. 32
3
Problem 8.
2 y+2
(6 x y
MATH 240Calculus III
Exam 2 Sample Questions
Z
Z
1. Evaluate the integral
Answer: 0.
0
ZZ
2. Evaluate the integral
Instructor: Dr. L.Wang
cos (y 2 ) dy dx by reversing the order of integration.
x
p
x x2 + y 2 dA , where D is the quarter of the unit disk
MATH 240Calculus III
Exam 1 Sample Questions
1. show that
y 2 sin2 y
= 0.
x0,y0 3x2 + y 2
2. Show that
x2 3y 4
does not exist.
x0,y0 3x2 + y 4
Instructor: Dr. L.Wang
lim
lim
3. Find the length of the curve given by r(t) = et cos t i + 2 j + et sin t k, f