MATH 2673 CRN 41986
Calculus III: Quiz 7
Name :
Fall 2009
Score :
Please use a pencil and show all work.
1. For t > 0, let
r(t) =< t2 , sin t t cos t, cos t + t sin t > .
Find the following:
(a) the unit tangent vector T(t),
(b) the unit normal vector N(t
MATH 2673 Code CRN 41986
Calculus III: Quiz 2
Name :
Fall 2009
Score :
/10
Please use a pencil and show all work.
1. Find a unit vector that points in the same direction as the vector from (5, 1, 0) to
(1, 2, 0).
2. Find u v.
(a) u =< 3, 9, 6 > and v =< 4
MATH 2673 CRN 41986
Calculus III: Quiz 3
Name :
Fall 2009
Score :
/10
Please use a pencil and show all work.
1. Find the terminal point of the vector < 1, 3, 4 > with initial point (2, 1, 0).
2. A tobaggan loaded with camping gear is pulled 500 ft across
MATH 2673 CRN 41986
Calculus III: Quiz 1
Name :
Fall 2009
Score :
/10
Please use a pencil and show all work.
1. Find the distance between the points (1, 3, 2), (3, 1, 1).
2. Find the vector from (4, 1, 0) to (1, 2, 0).
3. Describe in words the region repr
MATH 2673 CRN 41986
Calculus III: Exam 4
Name :
Fall 2009
Score :
/105
Note that exam is out of 105 points but you will only be graded out of 100 points. Read the exam carefully
and do the easiest problems rst. Show all work and use a pencil. Give exact a
MATH 2673 CRN 41986
Calculus III: Exam 2
Name :
Fall 2009
Score :
/105
Note that exam is out of 105 points but you will only be graded out of 100 points. Read the exam carefully
and do the easiest problems rst. Please show all work and use a pencil. Give
MATH 2673 CRN 41986
Calculus III: Exam 3
Name :
Fall 2009
Score :
/105
Note that exam is out of 105 points but you will only be graded out of 100 points. Read the exam carefully
and do the easiest problems rst. Show all work and use a pencil. Give exact a
MATH 2673 CRN 41986
Name :
Calculus III: Quiz 4
Fall 2009
Score :
/10
Please use a pencil and show all work. Be sure to write equations of planes in standard form.
1. Find parametric and symmetric equations for the line passing through the point (0, 4, 3)
MATH 2673 CRN 41986
Name :
Calculus III: Quiz 5
Fall 2009
Score :
/10
Please use a pencil and show all work. Be sure to write equations of planes in standard form.
1. Find an equation of a plane that has contains the point (1, 3, 10) and has normal
vector
MATH 2673 CRN 41986
Calculus III: Quiz 10
Name :
Score :
Please use a pencil and show all work.
1. Find the limit or show that it does not exist:
y2
.
(x,y )(0,0) x2 + y 2
lim
2. Find second partial derivatives of
f (x, y, z ) = z arctan(y/x).
3. Find the
MATH 2673 CRN 41986
Calculus III: Quiz 11
Name :
Fall 2009
Score :
Please use a pencil and show all work.
1. Use the chain rule to nd
M
u
and
M
v
where
2
M = xeyz , x = 2uv, y = u v, z = u + v
when u = 3, v = 1.
2. Find the directional derivative of
f (x,
MATH 2673 CRN 41986
Calculus III: Quiz 9
Name :
Fall 2009
Score :
Please use a pencil and show all work.
1. Find the length of the curve
r(t) =< et , et , t 2 >
from t = 0 to t = ln 3.
2. A ball is thrown at an angle of 45 degrees to the ground and lands
MATH 2673 CRN 41986
Calculus III: Quiz 8
Name :
Fall 2009
Score :
Please use a pencil and show all work.
1. Find the curvature of
r(t) = ti + t2 j + 2tk
at (2, 4, 4).
2. Let C be the curve with equations x = 2 t3 , y = 2t 1, z = ln t.
(a) Find the point a
MATH 2673 CRN 41986
Calculus III: Quiz 6
Name :
Score :
Please use a pencil and show all work.
1. Evaluate the integral:
1
0
4
2t
j+
k
2
1+t
1 + t2
dt
2. Find the limit. (Be sure to indicate any use of LHopitals rule.)
lim
t
arctan t, e2t ,
ln t
t
3. Find
MATH 2673 CRN 41986
Calculus III: Exam 1
Name :
Fall 2009
Score :
/105
Note that exam is out of 105 points but you will only be graded out of 100 points. Read the exam carefully
and do the easiest problems rst. Please show all work and use a pencil. Give