HW 5
Homework
Sec 8.1
WeBWorK.
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6.
.
Lab
Using integration by parts with
and
, gives
Welcome
12.
.
Using integration by parts with
and
the problem to an integral of the form
three more times reduces it down to integrating
20.
, reduces
. D
HW 3
Homework
34. Easy.
WeBWorK.
Quick
Grapher
52. Using the substitution
Table7.4, we calculated
so
and
Get Your
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Lab
Welcome
68. Completing the square
98. As Geoff showed we can view as a function of
use use the disk method. This gives
106. The m
CHEMISTRY 161
Chapter 1
Chemistry
arabic: al-kimya
greek: khymeia
latin: chimica
FUSION
~ 3,500 BC
Solar System Chemistry
Chemistry in Space
Amino Acids
Sugars
Star Formation
Star Destruction
ASTROBIOLOGY
PROPERTIES OF MATTER
physical
density
color
odor
c
Calculus II (Math 242) - Test 1
(No Work - No Credit)
Problem 1. [10 Points] Find the partial sum decomposition of
Problem 2. [6 Points] For :r > 0 we defined the natural logarithm as:
lnx=
j
I
. 1
dt
- .
t
State what it means that a function is 1-1, and
Calculus II (Math 242) Test 1
(No Work No Credit)
Problem 1. [10 Points] Find the partial sum decomposition of
r(x) =
x2 x + 3
.
(x2 + 4)(x + 1)
Problem 2. [6 Points] For x > 0 we defined the natural logarithm as:
Z x
dt
ln x =
.
t
1
State what it means t
HW 1
Homework
28a.
WeBWorK.
Quick
Grapher
Get Your
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28b. The two graphs intersect at
and
,
has slope and
has slope
. At
Lab
32.
Welcome
42. It is clear
is everywhere decreasing so it is one-toone. Its inverse is
.
.
48. must be one-to-one. We can s
Trigonometric Substitutions
Math 121 Calculus II
D Joyce, Spring 2013
Now that we have trig functions and their inverses, we can use trig subs. Theyre special
kinds of substitution that involves these functions. For these, you start out with an integral
t
Math 242 Midterm 2 Make-up
Due Apr 28, 2015
Instructions: This is most of the second midterm. If you got a problem
right on the midterm just write I got this one right on this makeup. Do
all the others. This is open book and you can ask Geo or me for help
252A HW March 19
Geo Patterson
March 19, 2015
Section 9.3
#6
Does the series converge or diverge? Give reasons for your answer.
2
n n
n=1
Solution: CONVERGES. Rewritten, the sum S equals:
S = 2
n=1
1
n3/2
1
Now the terms cfw_an = n3/2 are a sequence of p
252A HW February 5
Geo Patterson
February 5, 2015
Section 7.5
# 16
Solve the dierential equation
(sec x)
dy
= ey+sin x
dx
Solution: By separating the variables,
ey dy = cos(x)esin(x) dx
The left side is straight-forward to integrate. The right side can be
252A HW January 22
Geo Patterson
January 22, 2015
Section 7.2
# 16
Find the derivative of y with respect to t:
y = t ln t
Solution: Using the product rule and chain rule,
y =t
1
1/2
(ln t)
2
1
x
+
ln t
# 42
Evaluate the integral
/3
0
4 sin
d
1 4 cos
Sol
Math 252 Midterm 1
March 5, 2015
Help sheets are at the end.
(15)
1. A bacteria culture starts with 500 bacteria and after 4 hours there are
8000 bacteria.
a. Find the expression for the number of bacteria after t hours.
Solution: The general equation is
252A HW February 25
Geo Patterson
February 25, 2015
Section 8.3
# 18
Evaluate the integral
9 w2
dw
w2
Solution: Let w = 3 sin() then dw = 3 cos()d and the integral can be rewritten:
9 9 sin2
3 cos d
9 sin2
9 w2
dw =
w2
=
=
1 sin2 cos
d
9 sin2
cos2
d
HW 7
Homework
Sec 9.1
WeBWorK.
Get Your
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28.
Lab
.
Converges to 0.
Welcome
32.
.
Diverges.
60.
.
Converges to 0.
82.
.
Multiply the top and bottom by
simplify. The answer is .
106.
and
.
This sequence is nondecreasing and bounded above by .
Hence i
HW 9
Homework
Sec 9.5
WeBWorK.
Get Your
Grades
Lab
Welcome
4.
.
This diverges by the divergence test: the terms don't go to 0.
In fact they go to .
8.
.
Since
Since
this is is a geometrice series.
, it converges. In fact, it converges to
.
with
16.
.
Use
252A HW April 9
Geo Patterson
April 9, 2015
Section 9.7
#4
(a) Find the series radius and interval of convergence. For what values of x does the series
converge (b) absolutely? (c) conditionally?
1
X (3x
n=1
2)n
n
Solution: (a) By the Ratio Test,
un+1
(3x
CHEMISTRY 161
Chapter 3
1. Structure of an Atom
subatomic particles
electrons
(cloud)
protons
(nucleus)
m(n) / m(e) 2000
neutrons
(nucleus)
m(n) > m(p)
2. Atomic & Mass Number
mass number
(number of protons plus neutrons)
atomic number
(number of protons)
MATH 252A - Fall 2013
TA: Patrick Collins
Quiz 1
#1
Consider the function f x
x
1
3
x
4. Find df
1
dx at x
f 3 . [Hint: don't try to find a formula for f 1 .]
15
Solution
df
1
1
1
df
dx x 15 f 3
3x1
2
1
1
dx x 3
331
x3
2
1
1
.
13
#2
3
x1
Find dy dx if y
x
MATH 252A - Fall 2013
TA: Patrick Collins
HW 4 Solutions
7.4 #34
Find the derivative of y
tan
1
ln x .
Solution
dy
1
dx
2
1 ln x
1
1 ln x
ln x
1
x
2
1
x x ln x
d
dx
2
.
7.4 #52
2
Evaluate
2
dt
4 3 t2
.
Solution
We have
2
4 3t
2
Setting u
3 t gives 1
3 du
MATH 252A - Fall 2013
TA: Patrick Collins
HW 6 Solutions
7.6 #22
ln csc x
Find lim
x
2 x 2
2
.
Solution
Since both the numerator and the denominator go to zero as x
d
dx
2, we can use l'Hopital's rule. Since
1
d
csc x d x
ln csc x
csc x
sin x csc x cot x