First practice midterm
Midterm from 2011
1. A particle moves through three dimensional space
with velocity
1. A particle travels along the parametric curve
sin(2t), 2 t3/2 , cos(2t) . How far will the particle
3
travel between time t = 0 and t = 5.
v(t) =
First practice midterm
2
x
0
x 0
4xy
ez dz dy dx.
1. Find
2. Set up an integral in polar coordinates that nds
the volume above the xy-plane, below the plane z =
10 2x + 3y and between the cylinders x2 + y2 = 1
and x2 +y2 = 4. Evaluate the integral to nd t
First practice midterm
1. Find the directional derivative for the function
f(x, y, z) = xz2 3xy + 2xyz 3x + 5y 17 from the
point (2, 6, 3) in the direction of the origin.
f
f
2. Find
(0, 1) and
(0, 1) for
x
y
f(x, y) = sin x + y2 cos x + y4 arctan x(y2 1)
Chapter 12 problems from old nals
Fall 2011 - Original
3. Find the maximum and minimum of f(x, y) = xy
on the ellipse 3x2 + 4y2 = 1.
Spring 2012 - Administered
3. Let f(x, y, z) = x2 y3 z + 5z2 .
(a) Find a unit vector u in the direction in which f
increa
Chapter 11 problems from old nals
Spring 2012 - Administered
1. (a) Find a direction vector for the line of intersection of the planes x + 2y + z = 0 and x + y + 1 = 0.
(b) Find the equation of the plane containing the
line x = 2t, y = 1 t, z = 3t and the
Midterm 2 Student name: 1 (
Math 265 (Butler) Section: B
This test is closed book and closed notes. No calculator is allowed for this test. For full credit show all of
your work (legiblyl). Each problem is worth 10 points (a total of 50 points).
1. Wr