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
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?)
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
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 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 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 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 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
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
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
5. Determine the following limits if $11133 f (a?) : A and nihil f (4r) : B.
a. gamecc) 12. g1;I51_(f(w2)-f(w) c. mamax)
d. 11%1(f(w3)f(m) e. JENcc)
Solution: a. If a: < 0, then 3:2 > 0 and :r > 0. Therefore .332 a: > 0 for a: < 01 and
332-1? approaches 0
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
Solution: a. Assume c > 0. Then there is a positive integer m such that I/m is
the closest to (3 among all real numbers different from c and of the form 1/n where
c > 0. Then for any is > 0, we have
m
n is a positive integer. (Why?) Let :5 =
1
0 < [3: