


serve file  20220815T193017.736.pdf
serve_file__20220815T193017.736.pdf
Showing 58 out of 8
MA  261  Multivariate Calculus  exam MA 26100 ...
MA  261  Multivariate Calculus  exam MA 26100 EXAM 1 Form A September 29, 2016 NAME YOUR TA’S NAME STUDENT ID # RECITATION TIME 1. You must use a #2 pencil on the mark–sense sheet (answer sheet). 2. On the scantron, write 01 in the TEST/QUIZ NUMBER boxes and blacken in the ap propriate spaces below. 3. On the scantron, ﬁll in your TA’s name and the course number . 4. Fill in your NAME and STUDENT IDENTIF
MA  261  Multivariate Calculus  ...
MA  261  Multivariate Calculus  exam MA 26100 EXAM 1 Form A September 29, 2016 NAME YOUR TA’S NAME STUDENT ID # RECITATION TIME 1. You must use a #2 pencil on the mark–sense sheet (answer sheet). 2. On the scantron, write 01 in the TEST/QUIZ NUMBER boxes and blacken in the ap propriate spaces below. 3. On the scantron, ﬁll in your TA’s name and the course number . 4. Fill in your NAME and STUDENT IDENTIF
Page 5
5.
Find the length of the curve
~
r
(
t
)=
<t

sin
t,
1

cos
t>
on 0
≤
t
≤
π
. (Hint: use the
doubleangle formula cos(2
x
)=1

2 sin
2
x
.)
A. 4
B. 8
C.

4
D.

5
E. 2
π
6.
The curvature of the curve
~
r
(
t
)=
<
9 cos
t,
9 sin
t>
at
t
=
π
is
A. 9
B. 3
C.
1
9
D.
1
3
E. 1
5
Page 6
7.
If a particle has the given acceleration
~a
(
t
)=
<
2
,

cos
t,
3
4
√
t
>
with initial position
~
r
(0) =
<
0
,
1
,
1
>
and initial velocity
~v
(0) =
<
1
,
0
,
0
>
, then its position at
t
=
π
is
A.
<π
2
+
π,

1
,π
3
/
2
+1
>
B.
<π
2
+
π,

1
,π
3
/
2
>
C.
<π
2
,

1
,π
3
/
2
+1
>
D.
<π
2
+
π,
1
,π
3
/
2
+1
>
E.
<π
2
,
1
,π
3
/
2
+1
>
8.
Consider the function
f
(
x, y
)=
2+
xy
3
1+
x
2

y
2
on its maximal domain of deﬁnition. Calcu
late
lim
(
x,y
)
→
(0
,
0)
f
(
x, y
)
A. This limit does not exist.
B. This limit in not well deﬁned, since the function is not deﬁned at (0
,
0)
C. 0
D.
1
2
E. 2
6
Page 7
9.
Let
P
=
√
u
2
+
v
2
+
w
2
,
u
=
u
(
x, y
),
v
=
v
(
x, y
), and
w
=
w
(
x, y
).
If
u
(0
,
1) = 0,
u
x
(0
,
1) = 2,
w
(0
,
1) = 2,
w
x
(0
,
1) = 0, and
v
(
x, y
)=
ye
x
. Find
P
x
(0
,
1).
A. 2
·
5

1
/
2
B. 2
·
5
1
/
2
C. 5
1
/
2
D. 5

1
/
2
E. 4
·
5
1
/
2
10.
The total surface area of a cone having height
h
and a base radius
r
is
A
=
πr
√
r
2
+
h
2
+
πr
2
.
If
r
and
h
are measured as 3 in and 4 in, respectively, with an error in measurement of at
most 1 in each, use diﬀerentials to estimate the maximum error (in in
2
) in the calculated
surface area.
A. 2
.
4
π
B. 12
.
8
π
C. 15
.
2
π
D. 7
.
6
π
E. 3
.
8
π
7
Page 8
11.
Let
R
(
p, q
) = tan

1
(
pq
2
). Find
∂
2
R
∂q∂p
.
A.
2
q
(1

p
2
q
4
)
3
/
2
B.
2
q

2
q
5
p
2
(1 +
p
2
q
4
)
2
C.
q
(1

p
2
q
4
)
3
/
2
D.
2
q
(1 +
p
2
q
4
)
2
E.
q
2
(1

p
2
q
4
)
3
/
2
12.
Find the directional derivative for
T
(
x, y
)=
y

1
x

2
at (3
,

2) in the direction toward the
origin.
A. 7
B.

7
C.
7
√
13
D.

7
√
13
E. 5
8
Ace your assessments! Get Better Grades
Browse thousands of Study Materials & Solutions from your Favorite Schools
Purdue UniversityMain Ca...
Purdue_UniversityMain_Campus
School:
Multivariate_Calculus
Course:
Introducing Study Plan
Using AI Tools to Help you understand and remember your course concepts better and faster than any other resource.
Find the best videos to learn every concept in that course from Youtube and Tiktok without searching.
Save All Relavent Videos & Materials and access anytime and anywhere
Prepare Smart and Guarantee better grades
Students also viewed documents
lab 18.docx
lab_18.docx
Course
Course
3
Module5QuizSTA2023.d...
Module5QuizSTA2023.docx.docx
Course
Course
10
Week 7 Test Math302....
Week_7_Test_Math302.docx.docx
Course
Course
30
Chapter 1 Assigment ...
Chapter_1_Assigment_Questions.docx.docx
Course
Course
5
Week 4 tests.docx.do...
Week_4_tests.docx.docx
Course
Course
23
Week 6 tests.docx.do...
Week_6_tests.docx.docx
Course
Course
106