Exam 1 Solutions, MAC 3474, Honors Calculus 3, Fall15
1. Find an equation of the sphere centered at (1, 2, 3) that lies in the rst octant (all coordinates
are non-negative) and has the largest radius. Hint: Think of a similar problem for a circle in
Quiz 1 Solutions, MAC 3474 Honors Calculus III, Fall 2015
1. Find an equation for a sphere whose diameter is the straight line segment AB, where
A = (1, 2, 3) and B = (3, 2, 1).
Solution: A sphere is determined by its radius and center. Since AB is a diam
Placement Test, MAC 3474, Honors Calculus 3, Fall15
Show your work. Write your name on every piece of paper you turn in. Write you alias name on the
back of the exam sheet.
1-2. Find the limit or show that the limit does not exist:
Exam 3 Solutions, MAC 3474 Honors Calculus III, Fall15
1. Let f(x, y, z) = z x2 4y 2 . Sketch and/or describe the domain of f and sketch and/or
describe its level surfaces.
Solution: The square root exists only for non-negative numbers and therefore the d
Exam 2 Solutions, MAC 3474, Honors Calculus 3, Fall15
1. Sketch the curve traversed by the vector function
r(t) = cos t, sin t, sin(4t)
for 0 t /2 .
Indicate the orientation of the curve (the direction in which the curve is traversed).
Solution: The proje
Quiz 2 Solutions, MAC 3474 Honors Calculus III, Fall 2015
1. Sketch and/or describe the curves traversed by the vector function
r(t) = 2 sin(5t) , 4 , 3 cos(5t)
and identify the direction in which the curve is traced out as the parameter t increases.
Quiz 3 Solutions, MAC 3474 Honors Calculus III, Fall 2015
1. Find and sketch the domain of the function and describe its level sets
f(x, y) =
4 x2 y 2 + ln(x2 + y 2 1) .
Solution: The square root u is dened if u 0 and ln u is dened if u > 0. Therefore the
Vectors and the Space Geometry
Our space may be viewed as a collection of points. Every geometrical gure, such as a sphere, plane, or line, is a special subset of points in
space. The main purpose of an algebraic description of various objects
28. Double Integrals
28.1. The Volume Problem. Suppose one needs to determine the volume
of a hill whose height f (r) as a function of position r = x, y in the base
of the hill is known. For example, the hill must be leveled t
Dierentiation of Multivariable
16. Functions of Several Variables
The concept of a function of several variables can be qualitatively understood from simple examples in everyday life. The temperature in a room
may vary from point to po