CLASS QUIZ: JANUARY 31: PARTIAL FRACTIONS AND RADICALS
MATH 153, SECTION 55 (VIPUL NAIK)
Your name (print clearly in capital letters):
(1) Which of these functions of x is not elementarily integrable?
1
(A) x + x2
(B) x2 1 + x2
(C) x(1 + x2 )1/3
(D) x + x
CLASS QUIZ: JANUARY 14: INTEGRATION BY PARTS
MATH 153, SECTION 55 (VIPUL NAIK)
Your name (print clearly in capital letters):
In the questions below, we say that a function is expressible in terms of elementary functions or elementarily expressible if it c
REVIEW SHEET FOR MIDTERM 1
MATH 153, SECTION 55 (VIPUL NAIK)
To maximize eciency, please bring a copy (print or readable electronic) of this review sheet
AND the integration worksheet to the review session.
The document is arranged as follows. The initial
CLASS QUIZ: JANUARY 5: EXPONENTIAL GROWTH
MATH 153, SECTION 55 (VIPUL NAIK)
Your name (print clearly in capital letters):
(1) A species of unicellular micro-organisms doubles in number every one hour at room temperature and
remains constant when placed in
CLASS QUIZ: JANUARY 7: INVERSE TRIGONOMETRIC FUNCTIONS
MATH 153, SECTION 55 (VIPUL NAIK)
Your name (print clearly in capital letters):
(1) What is the domain of arcsin arcsin? Here, domain refers to the maximal possible subset of R on
which the function i
CLASS QUIZ: JANUARY 10: HYPERBOLIC FUNCTIONS
MATH 153, SECTION 55 (VIPUL NAIK)
Your name (print clearly in capital letters):
(1) What is the limit limx (cosh x)/ex ?
(A) 0
(B) 1/2
(C) 1
(D) 2
(E) The limit does not exist.
Your answer:
(2) What is the limi
REVIEW SHEET FOR FINAL
MATH 153, SECTION 55 (VIPUL NAIK)
To maximize eciency, please bring a copy (print or readable electronic) of this review sheet
AND the previous review sheet to the review session.
This review sheet does not repeat review of material
QUIZ ON INTEGRATION TECHNIQUES
MATH 15300, SECTION 21
This is a somewhat unconventional quiz. The questions here are not the sort that are likely to appear on
a test in this format, but (I hope) they are good for building your intuition, speed, and unders
QUIZ ON LIMIT COMPUTATIONS
MATH 15300, SECTION 21 (VIPUL NAIK)
Before doing these problems, make sure you thoroughly understand the routine problems in the homework.
These are intended only as additional problems and are not meant to be comprehensive.
1.
QUIZ ON SEQUENCES
MATH 15300, SECTION 21 (VIPUL NAIK)
This quiz contains a bunch of multiple choice questions to test your overall intuition regarding sequence.
1. Iteration
(1) Consider the sequence an = 2an1 , with a1 = , for , real numbers. What can we
APPLICATIONS QUIZ 1
MATH 15300, SECTION 21
This quiz has its focus on using the concepts in calculus you have learned so far in real-world situations
in other subjects: chemistry, economics, physics, biology, etc. In most cases, a simplied version of the
REVIEW SHEET FOR FIRST MIDTERM
MATH 15300, SECTION 21 (VIPUL NAIK)
1. Inverse trigonometric functions
Words .
(1) The functions sin, cos, tan, and their reciprocals are all periodic functions. While tan and cot have a
period of , the other four have a per
APPLICATIONS QUIZ 1 SOLUTIONS
MATH 15300, SECTION 21
This quiz has its focus on using the concepts in calculus you have learned so far in real-world situations
in other subjects: chemistry, economics, physics, biology, etc. In most cases, a simplied versi
CLASS QUIZ (TAKE-HOME): MARCH 9: TAYLOR SERIES AND POWER SERIES
MATH 153, SECTION 55 (VIPUL NAIK)
Your name (print clearly in capital letters):
For these questions, we denote by C (R) the space of functions from R to R that are innitely dierentiable every
CLASS QUIZ: MARCH 4: SERIES CONVERGENCE
MATH 153, SECTION 55 (VIPUL NAIK)
Your name (print clearly in capital letters):
(1) Consider
(A) It is
(B) It is
(C) It is
(D) It is
(E) It is
the series
nite and
nite and
nite and
nite and
innite.
1
k=0 22k
. What
CLASS QUIZ (TAKE-HOME): FEBRUARY 14: SEQUENCES AND MISCELLANEA
MATH 153, SECTION 55 (VIPUL NAIK)
Your name (print clearly in capital letters):
Please attempt these quiz questions prior to class and turn them in during class on Monday February 14.
(1) Cons
Calculus 153, Section 41
Instructor: Chris Skalit
Quiz 2
Name:
1. (5 points) Express the antiderivative as a function of x:
x3 x2 + 4 dx
Solution: We put x = 2 tan so that dx = 2 sec2 d and sec2 =
have
x3 x2 + 4 dx =
= 16
(sec2 1) sec2 (sec tan ) d
= 32
(
Calculus 153, Section 41
Instructor: Chris Skalit
Quiz 3
Name:
1. Compute the limits of the following sequences:
n2 + 1
n
4n2 + 3n
n2 + 1
1 + 1/n2
1
Solution: We have lim
= lim
=.
2 + 3n
n 4n
n 4 + 3/n
4
2+1
n
1
Hence, lim
=
2 + 3n
n
4n
2
(a) (2 points) l
Calculus 153, Section 41
Instructor: Chris Skalit
First Hour Exam
You have 50 minutes to complete the exam. The use of calculators, cellphones, notebooks,
etc. is strictly prohibited. Partial credit will be awarded for answers that are either incomplete o
Calculus 153, Section 41
Instructor: Chris Skalit
Quiz 5
Name:
1. (4 points) Explicitly compute the sum the of the series,
n=1
1
. Thus, we have
1x
xn =
Solution: We know that for |x| < 1, we have
n=0
n=1
22n1 1
=
5n
=
M
lim
M
n=1
M
lim
M
1
=
2
1
=
2
2
Calculus 153, Section 41
Instructor: Chris Skalit
Second Hour Exam
You have 50 minutes to complete the exam. The use of calculators, cellphones, notebooks,
etc. is strictly prohibited. Partial credit will be awarded for answers that are either incomplete
Supplemental Exercises for Math 153 (41) Spring 2013
1. Let f be dened on the closed interval,
3
2, 2
so that f (x) = sin x for all x dom(f ).
(a) Verify that f is an injective function.
(b) Compute (f 1 ) (x) for x (1, 1).
(c) How does your answer in pa
Calculus 153, Section 41
Instructor: Chris Skalit
Quiz 4
Name:
1. Compute each of the following limits:
x
3
(a) (2 points) lim 1 + 2
x
x
Solution: We are computing lim exp(x ln(1 + 3x2 ). From LHpitals Rule, we
o
x
get
ln(1 + 3x2 )
(1 + 3x2 )1 (6x3 )
= li
Calculus 153, Section 43
Instructor: Chris Skalit
First Hour Exam
You have 50 minutes to complete the exam. The use of calculators, cellphones, notebooks,
etc. is strictly prohibited. Partial credit will be awarded for answers that are either incomplete o
Supplemental Exercises for Math 153 (43) Spring 2012
1. (Added March 28) Let f be dened on the closed interval,
3
2, 2
so that f (x) = sin x for all x dom(f ).
(a) Verify that f is an injective function.
(b) Compute (f 1 ) (x) for x (1, 1).
(c) How does
Calculus 153, Section 43
Instructor: Chris Skalit
Final Exam
Name:
Instructions
1.
2.
3.
4.
5.
You have 2 hours to complete this exam.
Cellphones, notes, and calculators are prohibited.
You must write in INK. Ask the proctor for a pen if you dont have one
Calculus 153, Section 43
Instructor: Chris Skalit
Second Hour Exam
You have 50 minutes to complete the exam. The use of calculators, cellphones, notebooks,
etc. is strictly prohibited. Partial credit will be awarded for answers that are either incomplete
CLASS QUIZ: FEBRUARY 4 DELAYED TO FEBRUARY 7: DIFFERENTIAL
EQUATIONS
MATH 153, SECTION 55 (VIPUL NAIK)
Your name (print clearly in capital letters):
(1) Suppose a function f satises the dierential equation f (x) = 0 for all x R. Which of the
following is
CLASS QUIZ: JANUARY 19: MATHEMATICAL INDUCTION
MATH 153, SECTION 55 (VIPUL NAIK)
Your name (print clearly in capital letters):
For all these questions, natural number refers to positive integer. In particular, 0 is not considered to be
a natural number.
(