Math 122 - Fall 2016 - Homework - Chapter 5
Give complete, well written solutions to the following exercises:
1. Let
Z
J=
1
Z
1
x4
dx,
K=
0
1
Z
1+
x4
dx
and
0
L=
1
1 x8 dx.
0
Without evaluating the de
Section 7.1 Areas Between Curves
2010 Kiryl Tsishchanka
Areas Between Curves
We dene the area A of S as the limiting value of the sum of the areas of the above approximating
rectangles:
n
A = lim
n
i=
Math 122 - Summer 2016 - Midterm Exam 2 - Version A
You have 110 minutes to complete this midterm exam. Books, notes and electronic devices are not permitted.
Read and follow directions carefully. Sho
MATH-UA 122: Calculus II - Fall 2016 Instructor: Fanny Shum
Practice Exam 2
No calculators, notes, or other outside materials are permitted. Show all work to receive full credit.
1. Which of the follo
MATH-UA 122: Calculus II - Fall 2016 Section 004 Quiz 1: Oct 6, 2016
Name:_ Grade: / 10
No calculators, notes, or other outside materials are permitted. Show all work to receive full credit.
Multipl
Section 2.6 Implicit Dierentiation
2010 Kiryl Tsishchanka
Implicit Dierentiation
Some functions can be described by expressing one variable explicitly in terms of another
variable for example,
1x
y =
MATH-UA 122: Calculus II - Fall 2016 Section 004 Quiz 1: Sep 22, 2016
Name: Grade:
No calculators, notes, 01' other outside materials are permitted. Show all work to receive full credit.
/10
Multi
MATH-UA 122: Calculus II - Fall 2016
Section:
Worksheet 7: Area and Volumes
Name:
Date:
ONLY set up the integrals for each question.
1. Find the area of the region bounded by y = cos x, y = 2 cos x, f
Notes
Welcome, Review and the
Substitution Rule 5.5
Vindya Bhat
1/48
Class Plan
Notes
Announcements
Welcome
I
I
I
I
Syllabus review
Course calendar review
NYU Classes demo
WebAssign demo
5.4 The Fund
Math 122 - Summer 2016 - Final Exam - Version A
You have 110 minutes to complete this final exam. Books, notes and electronic devices are not permitted. Read
and follow directions carefully. Show and
MATHUA 122: Calculus 11 - Fall 2016 Section:
Name:
dx
1' A; (x+2)(x +5)
: J 4* \l. . 1 7L \3
\ i
U3?
f
a
9M
ay
Worksheet 6: Improper Integrals
Date: 2. Determine all p > 0 such that f 24 dx converges
Math 122 - Summer 2016 - Midterm Exam 1 - Version A
You have 110 minutes to complete this midterm exam. Books, notes and electronic devices are not permitted.
Read and follow directions carefully. Sho
Section 1.3 The Limit of a Function
2010 Kiryl Tsishchanka
The Limit of a Function
DEFINITION: We write
lim f (x) = L
xa
and say
the limit of f (x), as x approaches a, equals L
if we can make the valu
Section 2.1 Derivatives and Rates of Change
2010 Kiryl Tsishchanka
Derivatives and Rates of Change
The Tangent Problem
EXAMPLE: Graph the parabola y = x2 and the tangent line at the point P (1, 1).
So
Section 1.5 Continuity
2010 Kiryl Tsishchanka
Continuity
DEFINITION 1: A function f is continuous at a number a if
lim f (x) = f (a)
xa
REMARK: It follows from the denition that f is continuous at a i
Section 1.6 Limits Involving Innity
2010 Kiryl Tsishchanka
Limits Involving Innity
I. Innite Limits
DEFINITION: The notation
lim f (x) =
xa
means that the values of f (x) can be made arbitrary large
Section 2.4 The Product and Quotient Rules
2010 Kiryl Tsishchanka
The Product and Quotient Rules
THE PRODUCT RULE: If f and g are both dierentiable functions, then
d
d
d
[f (x)g(x)] = g(x) [f (x)] + f
Math 115 Formulas Sheet and Integration Techniques (Basic)
MATH 115 (S1)1
The following three groups of formulas are the most basic and frequently used formulas in Math 115,
please always keep in mind
Math 122 - Fall 2016 - Homework - Chapter 8
Give complete, well written solutions to the following exercises:
1. The Fibonacci sequence is defined by the equations
f1 = 1,
f2 = 1,
fn = fn1 + fn2 ,
n 3
MATH-LIA 122: Calculus 1i 3E1]! 2016 Sect.ion:_. Worksheet 1: Integration
I.
Name:_f_m_.m_ Date:
1. Which of the following re equai to
X [15 1133; dx? U '- \rn &U. r 9335'
Please cireie all of the afo
Math 122 - Fall 2016 - Homework - Chapter 6
Give complete, well written solutions to the following exercises:
1. Evaluate the following integrals. Indicate the technique(s) you are using.
Z
Z
sin x co
Notes
Integration by Parts 6.1
Vindya Bhat
1/20
Class Plan
Notes
Announcements
5.5 The Substitution Rule (Review)
6.1 Integration by Parts
Summary
2/20
Recall
Notes
Theorem (Substitution Rule)
If u
Section 8.7 Taylor and Maclaurin Series
Taylor and Maclaurin Series
In the preceding section we were able to nd power series representations for a certain restricted
class of functions. Here we invest
Section 8.2 Series
2010 Kiryl Tsishchanka
Series
DEFINITION: An innite series is an expression that can be written in the form
a1 + a2 + a3 + . . . + ak + . . .
The numbers a1 , a2 , a3 , . . . are ca
Section 8.1 Sequences
2010 Kiryl Tsishchanka
Sequences
Stated formally, an innite sequence, or more simply a sequence, is an unending succession
of numbers, called terms.
EXAMPLES:
(a) 0, 0, 0, 0, . .
Section 8.6 Representing Functions as Power Series
2010 Kiryl Tsishchanka
Representing Functions as Power Series
Consider
1
= 1 + u + u2 + u3 + . . . =
1u
EXAMPLE 1: Express
un
|u | < 1
n=0
(1)
1
as a
Section 8.5 Power Series
2010 Kiryl Tsishchanka
Power Series
DEFINITION: If c0 , c1 , c2 , . . . are constants and x is a variable, then a series of the form
cn xn = c0 + c1 x + c2 x2 + . . . + cn xn
Section 9.3 Polar Coordinates
2010 Kiryl Tsishchanka
Polar Coordinates
DEFINITION: The polar coordinate system is a two-dimensional coordinate system in which each
point P on a plane is determined by