MATH 138
Calculus II
Fall 2015
Course objectives. The goal of this course is to further expand your knowledge of calculus and its
applications for one-variable functions. The course can broadly be split into four parts. First, we will
continue where Calcu
Math 138: Assignment 5 Solutions
due Friday, October 17, 2014 at 4:00pm
1. Consider the Logistic model for population growth:
dy
y
= ry 1
dt
K
where y(t) represents a population at time t, r represents the intrinsic growth rate (that is,
the growth rate
Math 138: Assignment 8
due Friday, July 10, 2015 at 12:00 pm
1. Use the ratio test to determine whether the following series converge or diverge.
(a)
n=1
(2n)!
(n!)2
lim
n
Thus, by the ratio test
n=1
(b)
n=1
an+1
(2(n + 1)! (n!)2
= lim
n (n + 1)!)2
an
(2n
Notes:
1. Fill in your username and
student ID number.
2. Answer all questions in the
space provided. You may use
the last page as additional
space for solutions. Clearly
mark this if you do.
3. Your grade will be influenced
by how clearly you express
you
MATH 138
Assignment 9
Due at noon Friday March 27
Last Name :
First Name :
Student Id. #:
SECTION :
1- Find the radius and interval of convergence for each series:
(a) Section 11.8 #26 on page 746
(b) Section 11.8 #24 on page 746
(c)
n=0
(d)
n=1
n2
(x + 2
MATH 138
Assignment 8
Due at noon Friday March 20
Last Name :
First Name :
Student Id. #:
SECTION :
1- Determine whether the series converges or diverges. Remember to state the Theorem/Test used.
(a)
(1)k
k=1
(b)
j=2
j2
1
.
ln j
k2
k6 + 1
n=1
(d)
1
2
n
1
MATH 138
Assignment 10
Due at 3pm Thursday April 2
Last Name :
First Name :
Student Id. #:
SECTION :
1- Section 11.9 #16 on page 751
2- Section 11.10 #10 on page 765
3- Section 11.9 #40 (a) and (b) on page 752
4- Section 11.10 #28 on page 765
5- Section 1
MATH 138
ASSIGNMENT 0
Due Jan 13, 2015
LAST NAME (PRINT):
FIRST NAME (PRINT):
Student Id. #:
d
1dx
2-
SECTION :
3x+1
sin(t4 ) d t =
2x
cos2
dt
=
t 1 + tan t
sin t sec2 (cos t) d t =
3-
4
40
x
dx =
1 + 2x
1/2
51/6
6-
dt
=
cos2 t 1 + tan t
4 (e2x + 1)1 dx =
MATH 138
Assignment 7
Due at noon Friday March 13
Last Name :
First Name :
Student Id. #:
SECTION :
1- Determine whether the series converges or diverges. State the Theorem/Test used.
(a)
k=1
(b)
j=1
k3
k
.
+1
1
j3 j + 1
.
(c)
k=2
(d)
i=1
(1)k
ln k
.
k2
(
MATH 138
Calculus II
Winter 2015
Course objectives. This course is to further expand your knowledge of calculus of one-variable functions.
The goal is to continue where left o in Calculus I (MATH137) on integration. Various methods of integration
will be
MATH 138
ASSIGNMENT 3
Last Name :
Due at noon, Friday Oct. 9
First Name :
Student Id. #:
SECTION:
TUT #:
1. Sketch the region enclosed by the given curves and nd its area.
(a) y = x2 , y = 4x x2
(b) x = y 4 , y =
(c) y =
x2
,
4
2 x, y = 0
y = 2x2 , x + y
MATH 138
ASSIGNMENT 2
Last Name :
Due at noon, Friday Oct. 2
First Name :
Student Id. #:
SECTION:
TUT #:
1. An integrand with trigonometric functions in the numerator and denominator can often be converted
to a rational integrand using the substitution u
Math 138: Assignment 6
due Friday, June 26, 2015 at 12:00 pm
n
1
1000
1
, then
.
<
9
3n + 1 3
1000
n
1
1
(b) Given > 0, if n > , show that
< .
9
3n + 1 3
(c) What did we prove in part b)?
1. (a) Show that if n >
2. (a) Use the denition of the limit of a s
MATH 138
Assignment 5
Due at noon Friday Feb. 13
Last Name :
First Name :
Student Id. #:
SECTION :
1- Solve the following Initial Value Problem: y =
2- Section 9.3 #22
x2 y y
y+1
and
y(3) = 1
3- Review Chapter 9 #10
4- Suppose that a cup of freshly brewed
MATH 138
Assignment 1
Due by: 11 a.m., Friday, January 15.
Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a very good chance it will get lost. Print your name and I.D. number at the top of the rst page
MATH 138
Assignment 3
Due by: 11 a.m., Friday, January 29.
Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a very good chance it will get lost. Print your name and I.D. number at the top of the rst page
MATH 138
Assignment 2
Due by: 11 a.m., Friday, January 22.
Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a very good chance it will get lost. Print your name and I.D. number at the top of the rst page
MATH 138
Assignment 4
Due by: 11 a.m., Friday, February 5
Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a very good chance it will become lost. Print your name and I.D. number at the top of the rst pa
MATH 138
Assignment 6
Due by: 11 a.m., Friday, February 26
Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a good chance it will become lost. Print your name and I.D. number at the top of the rst page o
MATH 138
Assignment 5
Due by: 11 a.m., Friday, February 12
Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a very good chance it will become lost. Print your name and I.D. number at the top of the rst p
MATH 138
Assignment 7
Due by: 11 a.m., Friday, March 5
Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a good chance it will become lost. Print your name and I.D. number at the top of the rst page of yo
MATH 138
Assignment 10
Due by: 11 a.m., MONDAY, March 29
Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a good chance it will become lost. Print your name and I.D. number at the top of the rst page of
MATH 138
Assignment 9
Due by: 11 a.m., Friday, March 19
Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a good chance it will become lost. Print your name and I.D. number at the top of the rst page of y
MATH 138
Assignment 8
Due by: 11 a.m., Friday, March 12
Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a good chance it will become lost. Print your name and I.D. number at the top of the rst page of y
MATH 138
Things to know for the nal exam
Your nal exam on April 9 will include the broad spectrum of material that we have covered. More weight is placed on material since the mid-term. However, much of the later material depends on solid knowledge of ear
Sequences and their limits
Notes for MATH 138
1
The limit idea
For the purposes of calculus, a sequence is simply a list of numbers
x1 , x2 , x3 , . . . , xn , . . .
that goes on indenitely. The numbers in the sequence are usually called terms,
so that x1
MATH 138 Fall 2013 (Sec 002)
Additional exercises: Reduction Formulas
1.
(a) Derive the following reduction formulas for integers n 2:
Z
Z
1
n1
cosn2 x dx.
i.
cosn x dx = cosn1 x sin x +
n
n
Z
Z
1
n1
ii.
sinn x dx = sinn1 x cos x +
sinn2 x dx.
n
n
(For Se
Math 138
Assignment 8 Solutions
1. Determine whether the series is absolutely convergent, conditionally convergent, or
divergent.
X
n
(a)
(1)n1 2
n +4
n=1
X
n X n
n1
Solution: Consider
. Let an = n2n+4 and bn = n1 . Then
(1) n2 + 4 =
2+4
n
n=1
n=1
an
n/