MAT 266 Written Homework #9
9.3, 9.4
SOLUTIONS
Due: November 29
Solve the following problems, showing any necessary work.
1. [1 point] The graph of a hyperbola is x2 y 2 = 1. Find an equation in polar form for this hyperbola of
the form r = f ().
Solution
MAT 266 Written Homework #1
5.5, 6.1
SOLUTIONS
Due: September 6
Solve the following problems, showing any necessary work.
1. Find the following indenite integrals.
a. [1 point]
cos(2x) + x + e2x
dx
sin(2x) + x2 + e2x
du
Solution: Try u-Substitution with u
MAT 266 Written Homework #5
7.4, 7.5, 8.1
SOLUTIONS
Due: October 11
Solve the following problems, showing any necessary work.
1. [1 point] Set up (but do not evaluate) an integral whose value is the length of the curve y = sin x
between the points (0, 0)
MAT 266 Written Homework #4
7.1, 7.2, 7.3
SOLUTIONS
Due: October 4
Solve the following problems, showing any necessary work.
1. Let R be the region of the plane bounded by the curves y = 2x and 6x y = 8.
a. [1 point] Set up an integral that nds the area o
MAT 266 Written Homework #3
6.5, 6.6
SOLUTIONS
Due: September 27
Solve the following problems, showing any necessary work.
1. Determine whether the following integrals converge, and if they do, to what.
+
a. [1 point]
4
1
dx
x3
Solution:
+
4
1
dx = lim
b+
MAT 266 Written Homework #2
6.2, 6.3
SOLUTIONS
Due: September 13
Solve the following problems, showing any necessary work.
1. Find the following indenite integrals.
a. [1 point]
sec6 x tan8 x dx
Solution: Since the power of sec x is even and at least two,
MAT 266 Written Homework #6
8.2, 8.4, 8.5
SOLUTIONS
Due: October 25
Solve the following problems, showing any necessary work.
1. [1 point] Write down (and simplify) the rst three partial sums of the series
should be in fraction form
Solution: If you let a
MAT 266 Written Homework #7
8.6, 8.7
SOLUTIONS
Due: November 1
Solve the following problems, showing any necessary work.
1. [1 point] Find the rst four terms of the Taylor series of sin x at x =
.
4
Solution:
n
f (n) (x)
0
sin x
1
cos x
2
sin x
3
cos x
C. HECKMAN
SOLUTIONS
266
TEST 3A
2n 5
be a sequence starting with n = 1.
3n + 1
(a) [10 points] Does an converge? If so, to what?
(1) Let an =
Solution: Try to calculate lim an by letting n assume any real value in the formula:
n+
lim an = lim
n+
n+
2n 5
C. HECKMAN
SOLUTIONS
266
TEST 2A
(1) Let R be the region bounded by the curves x = 2, x = 3, y = 4 + sin(x), y = 2 + ln x.
(a) [10 points] Find the area of the region R. [1.73]
Solution: The region is sketched below, showing that LEFT = 2, RIGHT = 3, TOP
MAT 266 TEST 1A
SOLUTIONS
(1) Find the following integrals:
(a) [20 points]
x cos(4x) dx
Solution: Use Integration by Parts. Let u = x and v = cos(4x), so that u = 1 and v =
sin(4x)
cos(4x) dx =
. Then
4
x cos(4x) dx = x
sin(4x)
4
1
sin(4x)
x sin(4x) 1
d
MAT 266 Written Homework #8
9.1, 9.2
SOLUTIONS
Due: November 20
Solve the following problems, showing any necessary work.
1. Let C be the curve parameterized by the equations
x = 9t3 + 12t2 3t
y = 12t3 + 20t2 8t
0t1
a. [1 point] Find the coordinates of th
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