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 the direction of the vector = 2, 3, 1 ;
b [10 points] Th
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 the following:
= fy ;
c [10 points] The scalar equation
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.
Solution: This is homework problem 3 from section 13.3
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 and intermediate steps in order to get credit.
Solutio
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 intermediate steps in order to get credit.
Solution: We substi
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 ;
find the following:
c [10 points] The scalar equatio
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 work and intermediate steps in order to get credit.
The
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 intermediate steps in order to get credit.
Solution: We need
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 get credit.
Solution: Use determinants to compute this cr
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;
b [5 points] The coordinates of a vector 3AC AB;
c [5
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 such that x(0) = 1, x (0) = 2,
y(0) = 1, and y (0) = 3, an
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;
b [5 points] The coordinates of a vector 3AB AC;
c [5
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 line to the curve ~r(t) =
(t, t2 , t3 ) at t = 1.
3. Fin
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 find a Cartesian equation of the curve
x = ln t, y = t2
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 sucient just to write the answers. You must explain ho
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 versions
of a sample exam.‘ In problems that require reas
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 the direction of the vector = 1, 2, 3 ;
b [10 points] Th