MATH 2551-G MIDTERM 3
VERSION A
SUMMER 2025
COVERS SECTIONS 15.5-15.8, 16.1-16.8
Full name: GT ID:
Honor code statement: I will abide strictly by the Georgia Tech honor code at all times. I
will not use a calculator. I will not reference any website, application, or other CAS-enabled
service. I will not consult with my notes or anyone during this exam. I will not provide aid to
anyone else during this exam.
( ) I attest to my integrity.
Read all instructions carefully before beginning.
• Print your name and GT ID neatly above.
• You have 75 minutes to take the exam.
• You may not use aids of any kind.
• Show your work. Answers without work shown will receive little or no credit.
Question Points
1 2
2 2
3 2
4 2
5 2
6 2
7 4
8 6
9 8
10 10
11 10
Total: 50
, For problems 1-4 choose whether each statement is true or false. If the statement is always
true, pick true. If the statement is ever false, pick false. Be sure to neatly fill in the bubble
corresponding to your answer choice.
1. (2 points) If F(x, y) is a conservative vector field defined on all of R2 and C is any curve
!
in the plane, then C F · T ds = 0.
√
© TRUE FALSE
!!
2. (2 points) If S is a sphere in R3 and F is a constant vector field, then F · n dσ = 0.
S
√
TRUE © FALSE
3. (2 points) Given two circles centered at the origin, oriented counterclockwise, and any
vector field F, then the circulation of F is larger around the circle with larger radius.
√
© TRUE FALSE
4. (2 points) Suppose S is a smooth closed surface in R3 and F is a vector field whose
!!
components have continuous partial derivatives in R3, then S(∇ × F) · n dσ = 0.
√
TRUE © FALSE
5. (2 points) If f (x, y) is strictly positive at all points in R2, then
"" ""
f (x, y) dA < f (x, y) dA
R1 R2
whenever the area of R1 is smaller than the area of R2.
√
© TRUE FALSE
6. (2 points) If f : R → R is continuous on [0, 1], then
" 1 " 1 #" 1 $2
f (x)f (y) dx dy = f (x) dx
0 0 0
√
TRUE © FALSE
VERSION A
SUMMER 2025
COVERS SECTIONS 15.5-15.8, 16.1-16.8
Full name: GT ID:
Honor code statement: I will abide strictly by the Georgia Tech honor code at all times. I
will not use a calculator. I will not reference any website, application, or other CAS-enabled
service. I will not consult with my notes or anyone during this exam. I will not provide aid to
anyone else during this exam.
( ) I attest to my integrity.
Read all instructions carefully before beginning.
• Print your name and GT ID neatly above.
• You have 75 minutes to take the exam.
• You may not use aids of any kind.
• Show your work. Answers without work shown will receive little or no credit.
Question Points
1 2
2 2
3 2
4 2
5 2
6 2
7 4
8 6
9 8
10 10
11 10
Total: 50
, For problems 1-4 choose whether each statement is true or false. If the statement is always
true, pick true. If the statement is ever false, pick false. Be sure to neatly fill in the bubble
corresponding to your answer choice.
1. (2 points) If F(x, y) is a conservative vector field defined on all of R2 and C is any curve
!
in the plane, then C F · T ds = 0.
√
© TRUE FALSE
!!
2. (2 points) If S is a sphere in R3 and F is a constant vector field, then F · n dσ = 0.
S
√
TRUE © FALSE
3. (2 points) Given two circles centered at the origin, oriented counterclockwise, and any
vector field F, then the circulation of F is larger around the circle with larger radius.
√
© TRUE FALSE
4. (2 points) Suppose S is a smooth closed surface in R3 and F is a vector field whose
!!
components have continuous partial derivatives in R3, then S(∇ × F) · n dσ = 0.
√
TRUE © FALSE
5. (2 points) If f (x, y) is strictly positive at all points in R2, then
"" ""
f (x, y) dA < f (x, y) dA
R1 R2
whenever the area of R1 is smaller than the area of R2.
√
© TRUE FALSE
6. (2 points) If f : R → R is continuous on [0, 1], then
" 1 " 1 #" 1 $2
f (x)f (y) dx dy = f (x) dx
0 0 0
√
TRUE © FALSE
