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
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
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)
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)
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 pl
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 pr