Calculus 1 (Math-UA-121)
Fall 2015
Homework: Section 1.3
Give complete, well-written solutions to the following exercises.
Do not forget to write your name and discussion section number, and to staple your
solution.
1. For each function f and the given po

Calculus 1 (Math-UA-121)
Fall 2015
Homework: Section 1.4
Give complete, well-written solutions to the following exercises.
Do not forget to write your name and discussion section number, and to staple your
solution.
1. Evaluate the following limits. Justi

Calculus I Midterm Exam Detailed
Solutions
Time 70 minutes. Calculators, Textbooks and Notes are not allowed. You
DO NOT have to show work for the short answer section, which is worth 50%
of your grade. You MUST show work for the free response section, wh

Calculus 1 (Math-UA-121)
Fall 2015
Homework: Section 1.2
Give complete, well-written solutions to the following exercises.
Do not forget to write your name and discussion section number, and to staple your
solution.
1. Let f and g be linear functions with

Midterm Exam 2B
1. Suppose ln(x
a) e5 + 2
b) e5 2
c) e2 + 5
d) e7
Ans: C.
5) = 2. Solve for x
2. Let g(z) = sin
p
a) 2 3/3
b) p
1/2
c) 2/2
d) 0
e) 1/2
Ans: A.
1
(z). Find g 0 (1/2)
0
g (z) = p
1
1
z2
1
0
=) g (1/2) = q
1
3. Find the limit
lim x2 e
1
4
p
1

Calculus 1: Homework #9
1
Section 4.1
Exercise 28. Find the critical numbers of the function g(t) = |3t 4|.
Solution. The domain of g is all real numbers. Lets rewrite g as
3t 4, t 4 ,
3
g(t) =
3t + 4, t < 4 .
3
Then g 0 (t) is equal to 3 for t > 4/3 and

Calculus 1 (Math-UA-121)
Fall 2015
Homework: Section 1.1
Give complete, well-written solutions to the following exercises.
Do not forget to write your name and discussion section number, and to staple your
solution.
1. Find the domain and range of the fol

Section 1.1 HW
Please give complete, well written solutions to the following exercises.
1. For the following functions, nd f (3), f (4), and f (x + h), where h is
an arbitrary constant.
(1) f (x) = 4x2 3x + 7
x2 + 4x
(2) f (x) =
4x + 8
(3) f (x) = 4 x
x

Section 2.6 HW
Please give complete, well written solutions to the following exercises.
1. Consider the curve given by:
2y 3
y2
y 5 = x4 2x3 + x2
2
(a) Find the x-coordinates of all points where the curve might have a
horizontal asymptote.
(b) Find the

MATH 121.026 - CALCULUS I
Fall 2014 Syllabus
Tuesday Recitation Sections
Lecture
R
1
2
R
3
4
R
5
6
R
7
8
Day
T
W
M
T
W
M
T
W
M
T
W
M
Date
9/2
9/3
9/8
9/9
9/10
9/15
9/16
9/17
9/22
9/23
9/24
9/29
R
9
10
T
W
M
9/30
10/1
10/6
R
11
12
R
13
14
T
W
M
T
W
M
10/7

Section 3.5 HW
Please give complete, well written solutions to the following exercises.
The problems are from the textbook Exercises.
1. From section 3.5 #28, #34, #40, #42.
1

Section 4.7 HW
Please give complete, well written solutions to the following exercises.
1. Section 4.7 # 16
2. Section 4.7 # 22
3. Section 4.7 #38 (please give reasons for your answer)
4. Section 4.7 #54
1

Section 3.2 HW
Please give complete, well written solutions to the following exercises.
1. Using the properties of logs, calculate log10 (log10 10100 ) . Show all your
work. Only answer will not get any credit.
2. Section 3.2 # 28, # 38, # 60, #66, #78 (f

Section 3.4 HW
Please give complete, well written solutions to the following exercises.
1. A bacteria culture contains 200 cells initially and grows at a rate proportional to the size of the culture. After half an hour the population
has increased to 360

Section 2.1 HW
Please give complete, well written solutions to the following exercises.
1. Section 2.1 # 6, # 20, #30, #50.
2. Suppose f is dierentiable at x = a and g(x) = xf (x). Show that
g (a) = af (a) + f (a)
directly from the denition of the derivat

Section 3.5 HW
Please give complete, well written solutions to the following exercises.
The problems are from the textbook Exercises.
1. From section 3.5 #28, #34, #40, #42.
1

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 numbers for the following functions:
x x2
(a) f (x) = 4 +
3
2
3
2
(b) f (x) = 2x

Section 4.2 HW
Please give complete, well written solutions to the following exercises.
Please show all the steps - only answer will not get any credit.
1. Show that the equation x3 + ex = 0 has exactly one real root.
2. Show that the equation 3x + 2 cos

Section 1.2 HW
Please give complete, well written solutions to the following exercises.
1. Suppose the total cost of manufacturing q MP3 players is C(q) =
2q 2 3q +100 dollars. In one day, the number of MP3 players produced
in t hours can be modeled by th

Section 2.2 HW
Please give complete, well written solutions to the following exercises.
1. Consider the function f (z) =
6z 5:
(a) Find its derivative using the denition of the derivative.
(b) Find the equation of the tangent line for this function at the

Section 1.3 HW
Please give complete, well written solutions to the following exercises.
1. Consider the function shown below:
State the values of
(a) lim f (x)
x! 4
(b) lim + f (x)
(c) lim f (x)
x! 4
x! 4
(d) lim f (x)
(e) lim f (x)
+
(f) lim f (x)
(g) li

Section 1.5
Please give complete, well written solutions to the following exercises.
1. Find the values of a and b such that the
tinuous.
ax b
f (x) = 2x2 + 3ax + b
4
function given below is con-
x 1
1 < x 1
x>1
2. Use Intermediate Value Theorem to show t

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
+
x0
4. Find the limit:
x [1 + sin2
ax + 4 2
= 1.

Section 2.3 HW
Please give complete, well written solutions to the following exercises.
1. Show that the curves
y = x3 3x + 4 and y = 3(x2 x)
are tangent to each other. That is, that there is point where the
curves intersect and at this point the tangent

Section 2.5 HW
Please give complete, well written solutions to the following exercises.
1. Find the derivative of the function f (x) =
x2 +
1 + 4 x.
2. Find the derivative of the function f (x) = cos(3x) sec(1 x2 ).
3. Find the equation of the tangent lin

CORE-UA.107 Written HW 1
Due: Tuesday, September 20 during your recitation
Write full, clear solutions to the problems below. It is important that the logic of how you solved these
problems is clear. Although the final answer is important, being able to c

CORE-UA.107 QR: Probability, Statistics, and Decision Making, Written HW 2
Due: Tuesday, September 27 during your recitation
Write full, clear solutions to the problems below. It is important that the logic of how you solved these problems is clear.
Altho

CORE-UA.107 QR: Probability, Statistics, and Decision Making, Written HW 4
Due: Tuesday, October 11 during your recitation
Write full, clear solutions to the problems below. It is important that the logic of how you solved these
problems is clear. Althoug

CORE-UA.107 QR: Probability, Statistics, and Decision Making, Written HW 3
Due: Tuesday, October 4 during your recitation
Write full, clear solutions to the problems below. It is important that the logic of how you solved these
problems is clear. Although

CORE-UA.107 QR: Probability, Statistics, and Decision Making, Written HW 5
Due: Tuesday, October 25 during your recitation
Write full, clear solutions to the problems below. It is important that the logic of how you solved these
problems is clear. Althoug