Math 151, Homework #6
Matthew Thibault
Problems: (100 pts) Please solve the following problems. The rst group of problems are from the
textbook Calculus: One Variable (10th edition) by Salas, Hille, and Etgen. Do show your work,
and give clear arguments a
Example (1). Prove that
lim
x2
3x + 1 =
7
Proof. Let > 0. We want to show that there exists > 0 such that
0 < |x 2| < | 3x + 1 7| < .
First, because we are dealing with a squareroot, we have to impose a condition on how large can get.
Consider that in thi
Math 151, Section 32
Fall 13
HW 9 (the last one!)
Due: Tue, Dec 3
The following problems are for your practice only, dont hand them in.
From Section 4.4: 18, 24, 27, 30, 45.
From Section 4.5: 9, 17, 20, 24, 31, 35.
Hand in the following problems:
From Se
Math 151, Section 32
Fall 13
HW 6
Due: Tue, Nov 19
The following problems are for your practice only, dont hand them in.
From Section 3.5: 1-15, 18, 37, 40, 49.
From Section 3.6: 11, 18, 23, 29, 35, 46, 69.
From Section 3.7: 1-7, 17-20, 33-36, 45-47.
Hand
Math 151, Section 32
Fall 13
HW 4
Due: Tue, Oct 29
The following problems are for your practice only, dont hand them in.
From Section 2.4: 35, 37, 41, 42, 52.
Hand in the following problems:
From Section 2.4: 36, 38, 43, 44, 49 (hint: go back to the equi
Math 151, Section 32
Fall 13
HW 3
Due: Wed, Oct 23
The following problems are for your practice only, dont hand them in.
From Section 2.2: 5, 8, 23, 43, 50, 52.
From Section 2.3: 2, 3, 21, 35, 37, 41, 45-51, 61.
From Section 2.4: 1-7, 29.
Hand in the foll
Math 151, Section 32
Fall 13
HW 6
Due: Tue, Nov 12
The following problems are for your practice only, dont hand them in.
From Section 3.1: As many problems as you want to do.
From Section 3.2: 15, 18, 22, 33, 49, 53, 62, 69, 70.
From Section 3.3: 19, 20,
Math 151, Section 32
Fall 13
HW 5
Due: Tue, Nov 5
The following problems are for your practice only, dont hand them in.
From Section 2.5: 1-10, 17, 21, 23, 26, 31, 33, 34-37, 38, 39.
From Section 2.6: 1-5, 8, 13, 23, 30.
Hand in the following problems:
F
lo5lb
How close does 1 Med
#0 bt +o c +0 guWaniav
Si<l9+ 454' 27
I? I mm H(x)'9(2)\4 2, Icom whim was
i5 \x~?\ < 2-
2
For cfw_MM 2. 70, We ;5 box th C,L in hm-e,
OMAHA" Mia 2Q, S-b. W Ora/(1n 01" 3 a m'wlww
in ne box [MW Possiny 1: c) Sf-aujs in. m box
MIDTERM 2
There are two pages of problems for this exam. You are free to use any result
seen in class, the textbook or homework. Justify all the necessary steps citing the
proper results.
1. Please calculate the following limits:
(1) (5 points)
tan x
.
x0
Name:
Id #:
Math 153 (26) - Midterm Test 2
Spring Quarter 2016
Thursday, November 10, 2016 - 09:00 am to 09:50 am
Instructions:
Prob.
Points Score
possible
1
14
2
18
3
8
TOTAL
40
Read each problem carefully.
Write legibly.
Show all your work on these s
Name:
Id #:
Math 153 (26) - Midterm Test 1
Spring Quarter 2016
Thursday, October 20, 2016 - 09:00 am to 09:50 am
Instructions:
Prob.
Points Score
possible
1
8
2
18
3
14
TOTAL
40
Read each problem carefully.
Write legibly.
Show all your work on these sh
2
3+2 at the pornt (3,9).
2. Let m be the slope of the tangent line to the graph of y 2
Express m as a limit. (Do not compute m.)
Solutiou: The slope m of the tangent line to the graph of y : at) at the point
(339,f($n) is given by the limit
m : Hm f0?)
1
$_
2<5
Next we choose 5 in such a way that every a: satisfying the condition 0 <
1
lies in the solution set of E 2 < 5, and therefore the implication in (ic) holds. In
all three cases choosing a delta such that 0 < 5 S 1/2 1/(2 +3) = s/(4+2) ach
Math 15100-50 Midterm 1
Matthew Thibault
October 25, 2011
Instructions
Please read carefully.
This exam has a total of 60 points. Answers should be clear, well-organized, and precise. This
is a closed book exam. You are not allowed to use books, calculato
University of Chicago
Department of Mathematics
Math 151, Section 50
Midterm Exam #2 Solution Key
Tuesday, November 15, 2011
Last Name:
First Name:
UChicago ID Number:
Instructions. Please read carefully.
This exam has a total of 60 points. Answers should
Math 15100-50 Practice Final Exam
Matthew Thibault
December 1, 2011
Instructions
Please read carefully.
This exam has a total of 125 points. Answers should be clear, well-organized, and precise. This is
a closed book exam. You are not allowed to use books
Math 15100-50 Practice Final Exam
Matthew Thibault
December 1, 2011
Instructions
Please read carefully.
This exam has a total of 125 points. Answers should be clear, well-organized, and precise. This is
a closed book exam. You are not allowed to use books
Math 151, Homework #1
Matthew Thibault
Problems: (95 pts) Please solve the following problems. The rst group of problems are from the textbook
Calculus: One Variable (10th edition) by Salas, Hille, and Etgen. Do show your work, and give clear arguments an
Math 151, Homework #2
Matthew Thibault
Problems: (90 pts) Please solve the following problems. The rst group of problems are from the textbook
Calculus: One Variable (10th edition) by Salas, Hille, and Etgen. Do show your work, and give clear arguments an
Math 151, Homework #3
Matthew Thibault
Problems: (103 pts) Please solve the following problems. The rst group of problems are from the textbook Calculus: One Variable (10th edition) by Salas, Hille, and Etgen. Do show your work, and give clear
arguments a
Solutiou: a. For mat 0 we compute the derivative using the rules of differentiation:
f(z) = 0% (2:1: + 3:2 sin(1/$)= 2 + 2$sin(1/$) + 2:2 cos(1/:E) - (1/552)
33
for 3: ? 0.
For a: = 0 we must use the denition of the derivative:
, f(0+h)-f(0) , 2h+h23i11(1
14. Find all tangent lines to the graph of y 2 x3 that pass through the point (2, 4).
Solutiou: As dy/da: 2 d(a:3)/da: 2 3332, the equation of the tangent line through
a point (330,3:3) on the graph is y 3:0 2 3x301: 3:0). This line passes through
(2,4) e