Math M311
March 1, 2013
QUIZ #6 Solutions
Name: Matvei Libine
Given a function
f (x, y, z) = xy + x2 z + y 3 z 2
and a point
P = (3, 1, 1)
nd:
v
a [10 points] The directional derivative of f at P in t
Math M311
February 22, 2013
QUIZ #5 Solutions
Name: Matvei Libine
Given a function
f (x, y) = 8 + y ln(xy 11)
a [5 points] The partial derivative
f
x
= fx ;
b [5 points] The partial derivative
f
y
nd
Math M311
February 8, 2013
QUIZ #4 Solutions
Name: Matvei Libine
1 [10 points] Find the length of the curve
(t) = 2t + et + et ,
r
k
0 t 1.
Show all work and intermediate steps in order to get credit.
Math M311
February 8, 2013
QUIZ #4 Solutions
Name: Matvei Libine
1 [10 points] Find parametric equation of the tangent line to the curve
(t) = 3t2 , 4t, 2 t3 /3
r
at a point
(27, 12, 7).
Show all work
Math M311
February 1, 2013
QUIZ #3 Solutions
Name: Matvei Libine
1 [10 points] At what points does the curve (t) = t, 4 sin t, 4 cos t intersect the surface
r
x2 y 2 z 2 = 9. Show all work and interme
Math M311
February 22, 2013
QUIZ #5 Solutions
Name: Matvei Libine
Given a function
f (x, y) = 7 + x ln(xy 9)
a [5 points] The partial derivative
f
x
= fx ;
b [5 points] The partial derivative
f
y
= fy
Math M311
February 1, 2013
QUIZ #3 Solutions
Name: Matvei Libine
1 [10 points] Find the scalar equation of the plane passing through point (1, 2, 4) and parallel
to the plane 7x + 5y 3z = 1. Show all
Math M311
January 25, 2013
QUIZ #2 Solutions
Name: Matvei Libine
1 [10 points] Find the parametric equation of the line passing through points A = (6, 11, 1)
and B = (9, 4, 1). Show all work and inter
Math M311
January 25, 2013
QUIZ #2 Solutions
Name: Matvei Libine
1 [10 points] Compute the cross product b , where = 1, 1, 2 and b = 1, 2, 5 .
a
a
Show all work and intermediate steps in order to ge
Math M311
January 18, 2013
QUIZ #1 Solutions
Name: Matvei Libine
Given the points
A = (1, 2, 3),
B = (1, 4, 4)
and
C = (3, 3, 2),
nd the following:
a [5 points] The coordinates of vectors AB and AC;
Math M311 Practice Exam 2
Name:
Each question is worth 14 points.
1. If f (x, y) = (x2 + y 2 )2 , nd fxxy .
2. Find the tangent plane to z = eyx at (1, 1, 1).
3. If x and y are both functions of t suc
Math M311
January 18, 2013
QUIZ #1 Solutions
Name: Matvei Libine
Given the points
A = (3, 2, 1),
B = (4, 4, 0)
and
C = (5, 3, 1),
nd the following:
a [5 points] The coordinates of vectors AB and AC;
Math M311 Practice Exam 2
Name:
Each question is worth 14 points.
1. Find the area of the region inside the curve r = 2 sin and outside the
unit circle.
2. Find a parametric equation for the tangent l
Math M311 Practice Exam
Name:
Each question is worth 14 points.
1. Find the area of the parallelogram whose vertices are (1, 1, 1), (1, 2, 2),
(2, 3, 2), and (2, 2, 1).
2. Eliminate the parameter to f
DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF MASSACHUSETTS
Sample
MATH 233
EXAM 2
In problems that require reasoning, algebraic calculation, or the use of your graphing calculator,
it is not
MATH 233 Sample EXAM I 1_
The actual exam will contain ﬁve or stir: problems, in the format of one problem per page
(your work will be on the same page bellow the problem). Bellow you willﬁnd three ve
Math M311
March 1, 2013
QUIZ #6 Solutions
Name: Matvei Libine
Given a function
f (x, y, z) = xz + x2 y + y 2 z 3
and a point
P = (2, 1, 1)
nd:
v
a [10 points] The directional derivative of f at P in t