Notes
Functions 1.2
Vindya Bhat
[email protected]
September 8, 2015
Math 121
1/40
Class Plan
Notes
Announcements
1.1 Functions and their Representations
(Review)
1.2 Catalog of Essential Functions
Next Time
2/40
Student Survey (Clicker Question)
Notes

Section 4.4/4.2 HW
Please give complete, well written solutions to the following exercises.
1. Suppose that a function f is continuous on [0, 4], f (0) = 1, and f 0 (x) 7
for all x in (0, 4). What is the hightest possible value of f (4)?
2. Discuss the fo

Section 3.4 HW
Please give complete, well written solutions to the following exercises.
1. Section 3.4 #7) (from the textbook exercises)
2. Section 3.4 #10) (from the textbook exercises)
3. Section 3.4 #18)a) (from the textbook exercises)
1
Section 3.5 HW

Section 2.6 HW
Please give complete, well written solutions to the following exercises.
1. Consider the curve given by:
2y 3
y2
y = x4 2x3 + x2
2
(a) Find the x-coordinates of all points where the curve might have a
horizontal tangent.
(b) Find the y-co

Section 3.1 HW
Please give complete, well written solutions to the following exercises.
1
1. Sketch the graph of g(x) = 10 e2+x . Show your calculations or
4
explanations as to how you arrived at that sketch (e.g. table of values,
transformations etc.).
2

Section 1.6
Please give complete, well written solutions to the following exercises.
1. Find
3u4 + 5
u (2u2 + 2)(u2 + 1)
lim
2. Find all the horizontal and vertical asymptotes of the following two
functions:
sin2 x
x2 + 4
b) y = x2 + x |x|
a) y =
3. Sketc

Section 2.2 HW
Please give complete, well written solutions to the following exercises.
1. Consider the function f (z) =
3z 5:
(a) Find its derivative using the definition of the derivative.
(b) Find the equation of the tangent line for this function at t

Section 5.1 HW
Please give complete, well written solutions to the following exercises.
1. Section 5.1 # 6
2. Section 5.1 # 8
3. Section 5.1 # 10
1
HWL: practising problems from
earlier sections
Please give complete, well written solutions to the followin

Section 5.2 HW
Please give complete, well written solutions to the following exercises.
1. Section 5.2 # 6
2. Section 5.2 # 16
3. Section 5.2 # 34
1
Section 5.3 HW
Please give complete, well written solutions to the following exercises.
1. Section 5.3 # 2

Section 1.1 HW
Please give complete, well written solutions to the following exercises.
1. For the following functions, find f (3), f (4), and f (x + h), where h is
an arbitrary constant.
(1) f (x) = 6x2 + 2x 7
x
(2) f (x) = 4 + x +
2x + 5
f (x + h) f (x)

Section 4.1 HW
Please give complete, well written solutions to the following exercises.
Please show all the steps - only answer will not get any credit.
1. Find the critical points (f 0 (c) = 0 or f 0 (c) DNE) for the following
functions:
x2 x
(a) f (x) =

Product and Quotient Rules 2.4
Vindya Bhat
[email protected]
October 1, 2015
Math 121
1/31
Class Plan
Administrative
2.3 Basic Differentiation Formulas (Review)
2.4 Product and Quotient Rules
Next Time
2/31
Midterm 1 on October 15th
Date/Time: Thursday

Notes
Continuity 1.5
Vindya Bhat
[email protected]
September 17, 2015
Math 121
1/33
Class Plan
Notes
Announcements
1.4 Calculating Limits (Review)
1.5 Continuity
Next Time
2/33
Student Survey
(Clicker Question)
Notes
How many emails do you think I rece

Notes
Chain Rule and Implicit
Differentiation 2.5, 2.6
Vindya Bhat
[email protected]
October 6, 2015
Math 121
1/22
Class Plan
Notes
Administrative
2.4 Product and Quotient Rules (Review)
2.5 Chain Rule
2.6 Implicit Differentiation
Next Time
2/22
Midte

Notes
Linear Approximation and
Differentials 2.8
Vindya Bhat
[email protected]
October 8, 2015
Math 121
1/17
Class Plan
Notes
Administrative
2.5 Chain Rule (Review)
2.6 Implicit Differentiation (Review)
2.8 Linear Approximation and Differentials
Next

Notes
Limits 1.4
Vindya Bhat
[email protected]
September 15, 2015
Math 121
1/31
Class Plan
Notes
Announcements
1.3 The Limit of a Function (Review)
1.4 Calculating Limits
Next Time
2/31
Student Survey (Clicker Question)
Notes
Did you register your clic

Notes
Limits 1.3
Vindya Bhat
[email protected]
September 10, 2015
Math 121
1/30
Class Plan
Notes
Announcements
1.2 Catalog of Essential Functions (Review)
1.3 The Limit of a Function
Next Time
2/30
Student Survey (Clicker Question)
Notes
Did you regist

Notes
Differentiation Formulas 2.3
Vindya Bhat
[email protected]
September 29, 2015
Math 121
1/27
Class Plan
Notes
Administrative
2.1 The Derivative and Rates of Change
(Review)
2.2 The Derivative as a Function (Review)
2.3 Basic Differentiation Formu

Section 1.4 HW
Please give complete, well written solutions to the following exercises.
1. If
lim (f + g) = 2 and
xa
lim (f g) = 1
xa
Find
lim f g
xa
2. Find the value of a so that
lim
x0
3. Prove that lim+ x [1 + sin2
x0
4. Find the limit:
ax + 4 2
= 1.

Calculus 1 (Math-UA-121)
Fall 2016
Homework Week 2 Solutions
1. (6 pts) For each function f and the given point a below, find the limits lim+ f (x), lim f (x), lim f (x)
xa
xa
by evaluating the function at numbers close to a.
(a) a = 4, f (x) =
|x 4|
x4
S

Calculus 1 (Math-UA-121)
Fall 2016
1. Find the domain and range of the following functions:
(a) f (x) = 4 x4
Solution. To find the domain, we must make sure that 4x4 0, or, equivalently,
4 x4 . This means that x2 2. So, the domain of f is [ 2, 2] .
To f

Calculus 1 (Math-UA-121)
Fall 2016
Homework Week 1
Section 1.1 and 1.2
Name:
HAVE FUN!
1
Calculus 1 (Math-UA-121)
Fall 2016
Give complete, well-written solutions to the following exercises. Please show all your
work. You will submit a scan of your homewor

NYU-SH Calculus, Fall 2016 Answer Key for Exercise List 01
Quiz 01 will be on September 09
With this key the students can tell whether they had found correct answers.
It does not provide a complete solution as expected on quizzes and exams.
1. The domain

Virtual Advising & Registration
As you register for Fall courses, please
keep in mind:
Selected Fall classes may be changed based on Pre-Freshman Summer
program performance.
All HEOP and CSTEP freshmen must register for corresponding NonCredit Courses t

Virtual Advising & Registration
The College of Arts and Science has a team of
experienced academic advisors who work on
issues related to international students in the
College. Advisors help students adjust to the
College, work with issues related to inte

Calculus 1 (Math-UA-121)
Fall 2016
Homework - Week 2
Sections 1.3 and 1.4
Name:
Give complete, well-written solutions to the following exercises. Please show all your
work. You will submit a scan of your homework electronically through NYU Classes. Please