Math 182 Homework 8.3
Problem 12
Determine whether the series is convergent or divergent:
n=1
5 4 + n4 n n
We will use the integral test:
1
5 4 + 4 x x x
dx =
1
5x-4 + 4x- 2 dx = -
3
5 -3 1 x + 4x- 2 3
x=
=
x=1
5 -3 1 x + 4x- 2 3
x=1
Math 182 Homework 6.4
Problem 8
Consider f(x) =
2x (1+x2 )2 :
(a) Find the average value of f(x) on [0, 2] 2 2x Since the length of the interval is 2 this is 1 0 (1+x2 )2 dx. To do this we let u = 1 + x2 so that du = 2xdx. 2 (Notice the 2xdx in the numera
Math 182 Homework Section 6.5
Problem 12
A bucket that weighs 4lbs and a rope of negligible weight are used to draw water from a well that is 80 feet deep. The feet bucket is filled with 40lbs of water and is pulled up at a rate of 2 . However, water leak
Math 182 Homework Section 6.5
Problem 12
A bucket that weighs 4lbs and a rope of negligible weight are used to draw water from a well that is 80 feet deep. The feet bucket is filled with 40lbs of water and is pulled up at a rate of 2 . However, water leak
Calculus II Homework: Sequences
Page 1
1) (11.1.48) Find the first 40 terms of the sequence defined by an an even 2 3an + 1 an odd
an+1 =
and a1 = 11. Do the same if a1 = 25. Make a conjecture about this type of sequence. 2) (11.1.49) For what values of r
Review of Integration
Math 182 will formally begin with section 5.5. However, recitation sections during the first week will spend time with a review of sections 5.1-5.4 which set the stage for the Integral Calculus.
1
Differentiation
Since integration is
Math 182 Spring 2008
Greetings! Dear 182 Students, I am very pleased to be working with you this semester. I have been in the math department here at UNR since the fall of 1993 and I love all kinds of mathematics very very much. In addition to being a pro
Chapter 6 Exam Outline
The Chapter 6 Exam outline will take place on Wednesday March 5. Scientific Calculators only. To keep the length of the exam manageable, some problems will not require the integrals involved to be evaluated. However, unless noted, y
Homework 6.5 Extra Solutions
Problem 9
lbs A heavy rope, 50 feet long, weighs 0.5 foot and hangs over a building 120 feet high.
(a) How much work is done in pulling the rope to the top of the building? Adding up the weights of each little piece of rope an
Math 182 Homework 6.3
Problem 6
Graph the curve and find its exact length: x(t) = et + e-t y(t) = 5 - 2t 0 t < 3
We have that
dx dt
= et - e-t and
3
dy dt
= -2. Therefore, the exact length is
2 3
0
dx dt =
0
2
+
3
dy dt
dt =
0
(et - e-t ) + 4dt =
3 2
2
3
Math 182 Chapter 5 Exam
Graphing and symbolic algebra calculators are prohibited on the following exam. All necessary calculations must be shown. Unjustified answers will receive very little credit. With the exception of the numerical approximations
Math 182 Chapter 6 Exam Retakes
All work must be explained on the following exam. Unless otherwise noted, all answers must be exact. Calculators with graphing, symbolic or programmable features are not allowed.
AREA CALCULATION
Consider the region e
Math 182 Chapter 6 Exam
All work must be explained on the following exam. Unless otherwise noted, all answers must be exact. Calculators with graphing, symbolic or programmable features are not allowed. Be certain to do all trigonometric calculations
Homework 8.1
Problem 6
Find a formula for the general term an of the sequence, assuming that the pattern of the first few 1 3 4 terms continues: {- 4 , 2 , - 16 , 25 , . . . , } 9 The numerators are as follows: For a1 it is 1, for a2 it is 2, for a3
Math Homework 8.2
Problem 12
Determine if the geometric series is convergent. If it is convergent, then find its sum: 1 + 0.4 + 0.16 + 0.064 + . . . Notice that this geometric series has first term a = 1 and multiplier r = 0.4 since 0.4 = 0.16 0.064
Name_
M216 Calculus II Date_ M216 Review Sheet 4 1 Find a formula for the general term a of the sequence, assuming that the pattern of the first n few terms continues.
cfw_ 4, 9, 14, 19, .
a. a
n
= 5n + 1
b. a
n
= 1n + 5
c. a
n
= 1n
5
d. a
n
= 5n
1
2 Dete
Math 182 Homework Section 6.1
Problem 10
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical rectangle and then find the total area of the region.
Region bounded by y = x2 and y = 4x - x2 The
Math 182 Homework Section 6.2
Problem 8
Find the volume of the solid formed by taking the region enclosed by y = x 3 , x = 1 and y = 0 and rotating it around the y-axis. Notice that since 1 3 = 1 and 0 3 = 0 the boundaries of the region are at (0, 0) and
Math 182 Homework Section 6.2
Problem 8
Find the volume of the solid formed by taking the region enclosed by y = x 3 , x = 1 and y = 0 and rotating it around the y-axis. Notice that since 1 3 = 1 and 0 3 = 0 the boundaries of the region are at (0, 0) and