Math 2574H Honors Calculus III
NAME:
(Please print clearly)
Eighth Quiz (solutions)
16 Oct 2013
1. Each of the iterated integrals below represents a double integral over some region R .
For each one do the following:
(i) Shade the area or areas in the sup
Math 2574H Honors Calculus III
Fifth Quiz (solutions)
Due 30 Sep 2013
Consider a wire in the shape of a spiral curve with the following parametric equations:
x = sin( u ) u cos( u )
()
0 u 4 2
y = cos( u ) + u sin( u )
z = u
The force of gravity is given
Math 2574H Honors Calculus III
NAME:
(Please print clearly)
Fifteenth Quiz (solutions)
due 4 Dec 2013
1. Let S be the surface parametrized by r(u, v ) = cos u, sin u, u + v 2
and 0 v 2 .
with 0 u
(a) Find its surface area.
Ans: ru rv = sin u, cos u, 1 0,
Math 2574H Honors Calculus III
NAME:
(Please print clearly)
Seventh Quiz (solutions)
8 Oct 2013
1. Let z = f (x, y ) be a function whose partial derivatives are:
2y
z
=2
x
4x + y 2
and
2x
z
=2
.
y
4x + y 2
Let x and y be functions of s and t dened as foll
Math 2574H Honors Calculus III
NAME:
(Please print clearly)
Twelfth Quiz (solutions)
Due 18 Nov 2011
In the following, assume that the quantities in question (P and E ) are additive: one can
get the amount for the whole by adding the amounts from parts. D
Math 2574 Honors Calculus III
NAME:
(Please print clearly)
Tenth Quiz (solutions)
1. Find
Due 30 Oct 2013
2zx dV , where Q is the solid whose top boundary is the surface z =
xy ,
Q
the bottom is z = 0 and Q lies above the region R given by 0 y x , 0 x 1 .
Math 2574H Honors Calculus III
NAME:
(Please print clearly)
Sixth Quiz (solutions)
25 Sep 2013
1. Find the equation of each of the following planes:
(a) The plane that contains the point P = (3, 2, 1) and is perpendicular to the vector
n = 4i + 2j 3k.
Ans
Math 2574H Honors Calculus III
NAME:
(Please print clearly)
Second Exam (solutions)
11 Oct 2013
1. The gure below is a diagram of level curves of a function f (x, y ). On this gure:
(a) Circle the general area where | f (x, y )| is likely to be largest. (
Honors Calculus III
NAME:
(Please print clearly)
First Exam (solutions)
17 Sep 2013
A nal numerical answer does not need to be simplied, but its expression should not contain
any vectors. A nal vector answer must be a single vector whose individual compon
Math 2574H Honors Calculus III
NAME:
(Please print clearly)
Third Exam (solutions)
8 Nov 2013
1. The following iterated integral represents a double integral over some region R:
2
1
sin(x2 ) dx dy .
0
y/2
(a) Shade the area or areas in the supplied gure t
Math 2574H Honors Calculus III
NAME:
(Please print clearly)
Fourth Exam (solutions)
11 Dec 2013
1. Evaluate the following line integrals. In both cases C is the curve with parametrization
r(t) = 1 + 2 cos t, 2 sin t , 0 t /2 .
(y + xy ) ds
(a)
(y i + x j)
Math 2574H Honors Calculus III
NAME:
(Please print clearly)
Fourteenth Quiz (with solutions)
22 Nov 2013
1. For the vector eld F(x, y, z ) = x2 z i 2xy j + y 2 k .
F (the divergence of F ).
(a) Find
2
(x z ) +
(2xy ) + (y 2 ) = 2xz 2x
x
y
z
Ans:
F (the
Math 2574H Honors Calculus III
NAME:
(Please print clearly)
Thirteenth Quiz (solutions)
15 Nov 2013
1. Evaluate the scalar integral
(2x + y + z ) ds , over the curve C parametrized by
C
r(t) = (3 cos t) i + (3 sin t) j + 4t k, 0 t .
Ans: r (t) = (3 sin t)
Math 2574 Honors Calculus III
NAME:
(Please print clearly)
Ninth Quiz (solutions)
25 Oct 2013
(x2 + y 2 + x) dA, where S is the sector inside the circle r = 2, between the
1. Find
S
angles = 0 and = /4 (picture below). Hint: polar coordinates.
r=2
= /4
Math 2574H Calculus III
NAME:
(Please print clearly)
Second Quiz (solutions)
03 Sep 2013
1. Given the vectors v = 3, 1, 2
and w = 2, 0, 1 :
(a) Find v w, v v and w w.
Ans: v w = (3)(2) + (1)(0) + (2)(1) = 4, v v = (3)(3) + (1)(1) + (2)(2) = 14 and
w w = (
Math 2574 Honors Calculus III
NAME:
(Please print clearly)
Fourth Quiz (solutions)
13 Sep 2013
1. For a particle with acceleration a(t) = cos t, 2, 3t , plus initial values v(0) = 2 j and
r(0) = k , nd the formulas for v(t) and r(t) .
Ans: v(t) =
a(t) dt
Math 2574 Calculus III
NAME:
(Please print clearly)
First Quiz (solutions)
28 Aug 2013
1. Given the vectors u = 3, 1, 2
and v = 2, 2, 1 :
(a) Find the magnitudes |u| and |v| .
Ans: |u| = 9 + 1 + 4 = 14, |v| = 4 + 4 + 1 = 3.
(b) Find the vector 2u 3v .
Ans
Math 2574H Honors Calculus III
NAME:
(Please print clearly)
Third Quiz (solutions)
Due 9 Sep 2013
Express each vector answer as a single vector. The individual components of the vector do
not have to be simplied.
1. Find parametric equations for the line