Math 2411 Honors Calculus III Spring 2006, Georgia Tech
Mar 15, 2006
Midterm 2
1. Find the center of mass of a half disk of radius 1. 2. Find the volume of the ellipsoid variables).
x2 a2
Time: 50min
+
y2 b2
+
z2 c2
= 1 (Hint: Use a change of
Math 2401 M
Calculus III
Fall 2012, Georgia Tech
Quiz 10
1. Evaluate
C
Apr 12, 2012
Time: 15 minutes
y dx + xy dy where C is the parabolic path y = 2x2 from (0, 0) to (1, 2).
2. Use Greens theorem to compute the area bounded by the ellipse x2 /a2 + y2 /b2
Math 2401 M
Calculus III
Fall 2012, Georgia Tech
Quiz 9
Apr 5, 2012
Time: 15 minutes
1. Compute the area of the region bounded by the ellipse x2 /a2 + y2 /b2 = 1.
2. Integrate the vector eld (x2 , xy, z 2 ) along the segment of the helix (cos(t), sin(t),
Math 2401 M
Calculus III
Fall 2012, Georgia Tech
Quiz 8
March 15, 2012
Time: 15 minutes
1. Find the volume of the solid bounded by x + y + z = 1 and the coordinate planes.
2. Find the center of mass of a half-disk of radius 1.
Each problem is worth 6pts.
Math 2401 M
Calculus III
Fall 2012, Georgia Tech
Quiz 7
March 8, 2012
Time: 15 minutes
1. Use dierentials to estimate the volume of a right circular cone with base radius 7.2
centimeters and height 10.15 centimeters.
2. Find a function with gradient (y2 e
Math 2401 M
Calculus III
Fall 2012, Georgia Tech
Quiz 6
March 1, 2012
Time: 15 minutes
1. Find the maximum and minimum values of the function f (x, y) = x2 + 4y2 + x 2y over
the region enclosed by the ellipse 1 x2 + y 2 = 1.
4
2. Find the dimensions of a
Math 2401 M
Calculus III
Fall 2012, Georgia Tech
Quiz 5
Feb 23, 2012
Time: 15 minutes
1. Find a function with gradient (2xy, 1 + x2 ).
2. Find an equation for the tangent plane of the surface z = x2 + y2 at the point (1, 1, 2).
Each problem is worth 5pts.
Math 2401 M
Calculus III
Fall 2012, Georgia Tech
Feb 7, 2012
Quiz 4
Time: 15 minutes
1. Express the volume of the parallelepiped formed by the vectors (1, 0, 0), (1, 1, 0), (x, y, z )
as a function of 3 variables.
2. Compute the partial derivatives of z =
Math 2401 M
Calculus III
Fall 2012, Georgia Tech
Quiz 3
Feb 2, 2012
Time: 15 minutes
1. let r(t) be the position vector of a moving particle. Show that if the speed of the particle
is constant, then the velocity vector is perpendicular to the acceleration
Math 2401 M
Calculus III
Fall 2012, Georgia Tech
Jan 26, 2012
Quiz 2
Time: 15 minutes
1. Compute the unit tangent vector, and principal normal of the helix curve
r(t) := (cos(t), sin(t), t).
2. Compute the length of the helix for 0 t 2.
Bonus: Write an in
Math 2401 M
Calculus III
Spring 2012, Georgia Tech
Jan 19, 2012
Quiz 1
Time: 15 minutes
1. Find the angle between the diagonal of a cube and one of the edges (you
do not need to compute the numerical value).
2. Find an equation in x, y, z for the plane wh
Math 2401 L
Calculus III
Fall 2008, Georgia Tech
Final
Dec 11, 2008
Time: 180 minutes
1. Find the angle between the diagonal of a cube and diagonal of one of its sides.
2. Find the maximum and minimum values of f (x, y) = x2 + xy + y2 on the disk x2 + y2
Math 2401 M
Calculus III
Spring 2012, Georgia Tech
Mar 29, 2012
Midterm 2
Name:
Time: 60 minutes
Each problem is worth 15 points.
1. Find a function with gradient F(x, y) = 2xyi + (1 + x2 )j.
2. Find a normal vector to the surface z = x2 + y2 at the point
Math 2401 M
Calculus III
Fall 2012, Georgia Tech
Midterm 1
Name:
Feb 16, 2012
Time: 50 minutes
Each problem is worth 15 points.
1. Write an expression for the angle between the main diagonal of a cube and the diagonal
of one of its sides.
2. Find the equa
Math 2401 M
Calculus III
Fall 2012, Georgia Tech
Apr 19, 2012
Quiz 11
1. Find the area of the cone z =
2. Evaluate
Time: 15 minutes
x2 + y 2 from z = 0 to z = 1.
yz d where S is the rst octant part of the plane x + y + z = 1.
S
Each problem is worth 6pts.