Problem 1 (12 points). Compute the following limits. Briey justify the steps you take.
1 _ 2
- a:
(a) g 362 _ 4
(Z)
a W [i k» E
Mm ' W" E;
x23x2 fwg
b 1' - g: 39 - . ;
( ) $1311 9:2 + x 1 QTWEmWM (56ng
«it» w i 1 _ 2
Problem 2. [10 points] Give an 66 p
2. Use proof by contradiction to Show that Ex 6 Z such that 9M3? ~ 3).
gmoca 374 2 ' «swat ag 33. airing bi17%; E. ig'kirifi'
S
2. Let n be a positive integer. Use proof by smallest counterexample to show that
2 = n(n+ 1)(2n +1)
12+22+32~+~+n 6
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1
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w t
(7 1 , \m >4
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w TN 5> (50%)? U \W $33
Fall 2013 Calculus I - Homework 3 Solutions
Victor Allard
September 29, 2013
1
Problem 2.4.22
Using a , denition of a limit, prove that limx1.5
94x2
3+2x
= 6.
Step 1. Guessing a value for . Let > 0 be given. We have to nd a number > 0 such that
2
if 0 < |
Fall 2013 Calculus l Homework 4 Solutions
Dan Ginsberg
October 17, 2013
1 Problem 2.8.26
Find the derivative ofy) = i, and the domain ofg and g'.
The domain of g is L > 0, since we need i 2 {l for to make sense, and we
also need i, 7% 0. By definitiozi, w
Fall 2013 Calculus I - Homework 6 Solutions
Victor Allard
October 29, 2013
1
Problem 3.9.22
A particle moves along the curve y = 2sin( x ). As the particle passes through the point 1 , 1 ,
2
3
its x-coordinate increases at a rate of 10 cm/s. How fast is t
MATH 108
FALL 2013
FINAL EXAM REVIEW
Denitions and theorems. The following denitions and theorems are fair game
for you to have to state on the exam.
Denitions:
Limit (precise - version; 2.4, Def. 2)
Continuous at a number (2.5, Def. 1) and on an interv
MATH 108
FALL 2013
MIDTERM 2 REVIEW
The exam will cover everything weve covered in class from 2.7 up to and including the rst half of 5.4. Specically, everything in 5.4 that comes strictly
before Applications on p. 400 is fair game.
Denitions and theorems
Math 108 Calculus I
Practice Final
12/08/2010
Grading
PRINTED name:
1
2
Please circle your section:
(1)
T 1:30
Gilman 17
Ariturk, Sinan
(2)
T 3:00
Hodson 210
Tran, Timothy
(3)
Th 1:30
Maryland 309
(4)
Th 3:00
Hodson 316
Ravit, Jason
3
4
Tran, Timothy
Writ
Math 108 Calculus I
Midterm 2 Practice 11/10/2010
Print your name here:
Grading
1
Please circle your section:
(1)
T 1:30
Gilman 17
Ariturk, Sina
(2)
T 3:00
Hodson 210
Tran, Timothy
(3)
Th 1:30
Maryland 309
(4)
Th 3:00
Hodson 316
Ravit, Jason
2
3
Tran, Tim
Math 108 Calculus I
Midterm I Practice 10/07/2010
Print your name here:
Grading
1
Please circle your section:
(1)
T 1:30
Gilman 17
Ariturk, Sina
(2)
T 3:00
Hodson 210
Tran, Timothy
(3)
Th 1:30
Maryland 309
(4)
Th 3:00
Hodson 316
Ravit, Jason
2
3
Tran, Tim
Homework 2: solutions
Section 1.2
39. f f (x) = sin(sin(x), Dom(f f ) = R.
f g (x) = sin(1 x), Dom(f g ) = Dom(g ) = [0, +).
g f (x) = 1 sin x, Dom(g f ) = cfw_x : sin(x) > 0 =
= [2, ] [0, ] [2, 3 ] = nZ [2n, 2(n + 1) ].
56. With v = 350mi/h and h = 1mi:
Homework 3: solutions
Part I
A1. For a real number, the points corresponding to and on the unit circle are symmetric
2
with respect to the line x = y (the line of slope 1 passing through the origin). Therefore their (x, y )
coordinates are reversed: cos()