Calculus II (Math 141), UMass Boston
Homework on Lecture 7
Quiz time/date will be announced in class
1.
Find a linearsubstitution (via completing the square) to transform the radical to a multiple of an expression of the form
u2 1 or 1 u2 .
(a) x2 + x +
Tuesday, November 3, 2015
8:09 PM
Calculus2Session1 Page 1
Calculus2Session1 Page 2
can you explain how : 3x5 became
right after integral of 3x+61?
Calculus2Session1 Page 3
l2/Ol
MATH 141 Sample Final anm
Show all work, ' MATH l 41 CALCULUS u . No books,
aplain each step. SAMPLE FINAL EXAMINATION no notes.
Part A. Do all four of the problems.
1. Find the ﬁrst derivative of each function. Note. arcsin a sin“. etc.
a) y = arc
THE FIRST HOUR EXAM WILL BE HELD ON MONDAY, OCTOBER 5, IN LIPKE AUDITORIUM. IT will
cover material in Assignments 14; most of the questions will resemble homework
questions. There will be a REVIEW for the exam on Friday, October 2.
You should
Chapter 2:
HOUR EXAM
PHYSICS 113
1
lf you want your exam returned privatelv, check
201 5
here:
!
There are two pages of questions, and formulas on page 2. Show_your calculations and substltutions,.and express your answers to
2 or 3digit accuiacy, in p.Igp.gllldlC.
1Pointers for Hour Exam 2
One way to measure the normal force is with a device found in bathrooms,
and used by weightwatchers. This can be imagined as massless and lying
between the object and the surface in question.
When friction is absent for a roller
NANYANG
TECHNOLOGICAL
UNIVERSITY
SEMESTERI EXAMINATION 2OTO201T
MAS zLL  Calculus III
December2010
MAS 211
TIME ALLOWED: 2 hours.
Solutions
Question 1
(20 Marks)
Determine whether the following seriesare convergentor divergent.
Justify your answers.
oo
Calculus II (Math 141), UMass Boston
Homework on Lecture 21
Quiz time/date will be announced in class
1. Plot the number z on the complex plane (you may use one drawing only for all the numbers). Find all real numbers and for
which z = e+i . Your answer m
Calculus II (Math 141), UMass Boston
Homework on Lecture 11
Quiz time/date will be announced in class
x
1. Match the graphs of the parametric equations x = f (t), y = g(t) with the graph of the parametric curve :
y
y
x
1
t
1
(a)
= f (t)
= g(t)
1
t
1
t
(
Calculus II (Math 141), UMass Boston
Homework on Lecture 8
Quiz time/date will be announced in class
1. Compute the limits. The answer key has not been fully proofread, use with caution.
(a) lim
sin x
.
x
(b) lim
x
.
ln(1 + x)
(i) lim
x
1
.
x 1 ln x
(j) l
Calculus II (Math 141), UMass Boston
Homework on Lecture 13
Quiz time/date will be announced in class
1. Give a geometric definition of the cycloid curve using a circle of radius 1. Using that definition, derive equations for the cycloid
curve. Find area
Calculus II (Math 141), UMass Boston
Homework Prerequisite Exponential Function Topics
Quiz time/date will be announced in class
1. Differentiate.
x
(d) xx .
x
x
x
answer: (ln(x)2 xx +x + xx +x1 + (ln x)xx +x
answer: 3(ln 10)x2 (10)x
3
(e) (sin x)cos x .
Calculus II (Math 141), UMass Boston
Homework on Lecture 3
Quiz time/date will be announced in class
1. Evaluate the indefinite integral. Illustrate the steps of your solutions.
Z
Z
(f)
x2 e2x dx.
(a)
x sin xdx.
2 2x
2x
2x
answer: x e
xe
e
+C
2
2
4
answ
Calculus II (Math 141), UMass Boston
Homework on Lecture 6
Quiz time/date will be announced in class
1. Integrate.
Z
1
dx.
(a)
3 + cos x
3 tan x + 1
1
2
+C
answer: arctan
2
2 2
5
ln (sin x + 2 cos x) +
x+C
2
2
5
15
dx
.
2 sin x cos x + 5
answer:
arctan
Calculus II (Math 141), UMass Boston
Homework on Lecture 12
Quiz time/date will be announced in class
1. Find the values of the parameter t for which the curve has horizontal and vertical tangents.
(a) x = t2 t + 1, y = t2 + t 1
answer: horiz.: t = 1 , ve
Calculus II (Math 141), UMass Boston
Homework on Lecture 19
Quiz time/date will be announced in class
1. Determine the interval of convergence for the following power series.
(a)
X
(x 2)n
.
3 n+1
n=1
answer: x [1, 3).
X
10n xn
(b)
.
n3
n=1
h
i
answer: x 1
Calculus II (Math 141), UMass Boston
Homework on Lecture 1
Quiz time/date will be announced in class
1. Let x (0, 1). Express the following using x and
1 x2 .
(e) sin(2 arccos(x).
q
answer: 2x 1 x2
(a) sin(arcsin(x).
answer: x
(b) sin(2 arcsin(x).
(f) sin
R
Q= fR
cfw_=fRd4f
R4r/9= Rr
ecfw_,rvg or
.^
E= FlR,r
Acflo/v
,LlW/1ed4*
L*y;*
'l
I
i
t
v
ll RDT+rr*vat Ea>h
\ zq, = t*, I
( f ='%MN"i,cfw_ln

*
&cfw_0N'7 :r
t^*.
'lcfw_O
r.r
A
=
lrr64r
'Y3 lgf
f+r="
+4
]3ex
(
/
\[r
Y
\P
N
t,
eut_.,
.rl
f q,
[.,
tlANDouT
PHYSICS
113
7
October 5  9, 2015
ASSIGNMENT 5
READING: Chapter 12, Sec 1; Chapter4, Secs. 7,8; Chapter 5, Sec. 1
HOMEWORK
in the diagonal cord 8S F,
cord and the weight and mass of the suspended object.
the horizontal
1. n Fig. 1 251, pg 331, t
Calculus II (Math 141), UMass Boston
Homework on Lecture 12
Quiz time/date will be announced in class
1. Find the values of the parameter t for which the curve has horizontal and vertical tangents.
(a) x = t2 t + 1, y = t2 + t 1
answer: horiz.: t = 1 , ve
Calculus II (Math 141), UMass Boston
Homework on Lecture 13
Quiz time/date will be announced in class
1. Give a geometric definition of the cycloid curve using a circle of radius 1. Using that definition, derive equations for the cycloid
curve. Find area
Calculus II (Math 141), UMass Boston
Homework on Lecture 12
Quiz time/date will be announced in class
1. Find the values of the parameter t for which the curve has horizontal and vertical tangents.
(a) x = t2 t + 1, y = t2 + t 1
answer: horiz.: t = 1 , ve
Calculus II (Math 141), UMass Boston
Homework Review problems for the final
This is a subset of the Master Problem Sheet
1. Problems that have appeared past final(s):
(a) Problem 2.m.
(b) Problem 4.a.
(c) Problem 6.d (the problem was formulated slightly d
Calculus II (Math 141), UMass Boston
Homework on Lecture 9
Quiz time/date will be announced in class
1. Determine whether the integral is convergent or divergent. Motivate your answer.
Z
1
(a)
(x 1)
2
3
2
dx.
(l)
2
xex dx.
answer: convergent
Z
answer: con
Calculus II (Math 141), UMass Boston
Homework on Lecture 16
Quiz time/date will be announced in class
1. Express the infinite decimal number as a rational number.
(a) 0.9 = 0.99999 . . .
answer: 118
99
(e) 0.09 = 0.0909090909 . . . .
answer: 1
(b) 1.6 = 1
Calculus II (Math 141), UMass Boston
Homework on Lecture 20
Quiz time/date will be announced in class
(a) A tank contains 30 kg of salt dissolved in 10000 liters of
water and salt solution. Brine that contains 0.05 kg of salt
per liter enters the tank at
Calculus II (Math 141), UMass Boston
Homework on Lecture 4
Quiz time/date will be announced in class
1. Integrate. Illustrate the steps of your solution.
Z
1
dx
(a)
x+1
Z
(h)
x
dx
2x2 + x + 1
7 arctan 4x+1
+C
answer: 1 ln x2 + 1 x + 1
4
2
2
14
7
answer: