MATH 127 WORKSHEET 3
(1) Consider the function
f (x) =
(x
x+2
2)3
if x < 2
if x 2.
Is f continuous at x = 2? Is f dierentiable at x = 2?
(2) Find the derivatives of the following functions:
2
(a) x 3 tan(x)
3
(b) (5x + 3x
(c)
x2
2x
2
4)
p
3
x
1
x
4x
x3
x+
MATH 127 Fall 2016
Worksheet #2
(1) Suppose that a capacitor is initially uncharged, and is connected to a constant voltage
source in an RC (resistor-capacitor ) circuit at time t = 0. The charge on the capacitor
is then given by
Q(t) = CV (1
e
t
RC
) cou
[3]
[3]
[3]
[3]
MATH 127 Final Examination.
2. Evaluate the following limits.
2
. I +4
(a) xlgxolz2+z+2
(h) lim tans:
gigd] I
. 1- 1.
(L) 1:133? 11.:
(d) iim cfw_sin :45)u
xow
Fall Term 2009
Page 3 of 10
UNIVERSITY OF WATERLOO
TEST # 1
FALL TERM 2008
Student Name (Print Legibly)
(family name)
(given name)
Signature
Student ID Number
COURSE NUMBER
MATH 127
COURSE TITLE
Calculus 1 for the Sciences
COURSE SECTION(s)
001 002 003 004 005 006 007 008 009 010
DA
MATH 127 Fall 2013
Assignment 9
Topics: Newtons method, antiderivatives, denite/indenite integrals, Fundamental
Theorem of Calculus, and Riemann sums
Due: 12:00 pm, Wednesday, November 20th
Instructions:
Print your name and I.D. number at the top of the
MATH 127 Fall 2013
Assignment 5
Topics: Limits, derivatives, continuity, intermediate value theorem, tangent lines
Due: Wednesday October 16th
Instructions:
Print your name and I.D. number at the top of the rst page of your solutions, and underline
your
MATH 127 Fall 2013
Assignment 3
Topics: Exponentials, logarithms, and inverses
Due: 12:00 pm, Wednesday, October 2nd
Instructions:
Print your name and I.D. number at the top of the rst page of your solutions, and underline
your last name.
Submit your so
MATH 127 Fall 2013
Assignment 4
Topics: Trig functions, inverse trig functions, limits
Due: 12:00 pm, Wednesday October 9th
Instructions:
Print your name and I.D. number at the top of the rst page of your solutions, and underline
your last name.
Submit
Fall 2013 MATH 127 Calculus 1 for the Sciences
Instructors/Sections:
Sec.
Time
Room
Instructor
Oce/E-mail
001
9:3010:20
DWE 3522
Anton Baglaenko
MC [email protected]
002
10:3011:20
MC 4020
Clinton Loo
M3 [email protected]
003
1:302:20
MC
MATH 127 Fall 2013
Assignment 6
Topics: Power rule, product rule, quotient rule, chain rule, logarithmic dierentiation,
implicit dierentiation
Due: 12:00 pm, Wednesday, October 30th
Instructions:
Print your name and I.D. number at the top of the rst page
MATH 127 Fall 2013
Assignment 8
Topics: LHopitals Rule, curve sketching, optimization
Due: Wednesday November 13th
Instructions:
Print your name and I.D. number at the top of the rst page of your solutions, and underline
your last name.
Submit your solu
MATH 127 Fall 2013
Assignment 7
Topics: Exponential growth and decay, related rates, max/min, linear approximation,
dierentials
Due: 12:00 pm, Wednesday, November 6th
Instructions:
Print your name and I.D. number at the top of the rst page of your soluti
MATH 127 Fall 2013
Assignment 1
Topics: Inequalities, absolute value, lines, circles, parabolas.
Due: 12:00 pm, Wednesday, September 18th
Instructions:
Print your name and I.D. number at the top of the rst page of your solutions, and underline
your last
Math 127 Winter 2016
Assignment #9: Related Rates, Optimization, Mean Value
Theorem
Due Monday, March 28th at noon in the drop boxes outside MC 4066
Instructions:
Print your name and I.D. number at the top of the first page of your solutions.
Unde
UNIVERSITY OF WATERLOO
TEST # 1
FALL TERM 2009
Student Name (Print Legibly)
(family name)
(given name)
Signature
Student ID Number
COURSE NUMBER
MATH 127
COURSE TITLE
Calculus 1 for the Sciences
COURSE SECTION(s)
001 002 003 004 005 006 007 008 009
DATE O
UNIVERSITY OF WATERLOO
TEST # 1
FALL TERM 2010
Student Name (Print Legibly)
(family name)
(given name)
Signature
Student ID Number
COURSE NUMBER
MATH 127
COURSE TITLE
Calculus 1 for the Sciences
COURSE SECTION(s)
001 002 003 004 005 006 007 008 009
DATE O
MATH 127 Fall 2013
Assignment 2
Topics: Functions, graphs, domain, range, function composition, and exponentials
Due: 12:00 pm, Wednesday September 25th
Instructions:
Print your name and I.D. number at the top of the rst page of your solutions, and under
MATH 127 Final Examination. Fall Term 2009 Page 4 of 10
3. The rate of decrease of the amount of a certain medicine in a patients bloodstream is
proportional to the amount of medicine present in the bloodstream.
[2] (a) If m(t) = Flue"It is the amount of
MATH 127 _ Final Examination. Fall Term 2009 Page 10 of 10
ROUGH WORK and IDENTITIES
cfw_You may tear off this sheet it will not. be marked.)
1sincfw_A:|:B=sinAcosB:|:cosAsinB => sin29=25i119c059
ms 26' = (5052 9 Sinai?)l
2 CDS(A:I:B)=CDSACOSBIISinAL-ii
MATH 127 Final Examination. Fall Term 2009 Page 9 of 10
[4] 8. 1 A circular disk of radius 1" is used in an evaporator and is rotated in a vertical plane. It
is to be partially submerged in the liquid so as to maximize the exposed wetted area. of the
disk
MATH 127 ~ Final Examination. Fall Term 2009 Page 3 of 10
T. (Applications of integration.) Consider the region R bounded by the curves 1; = :c y = 1; I,
and .7: = 2
[5] Ea.) Sketch R in the zyplane and nd its area.
[5] [b] What is the volume of the solid
l2l
l2]
[2]
[3]
l3]
l2]
l-iA'l'l-l 127 - Final Examination. Fall 'l'ern'l 20:19
Page '2 el' 10
l. Various Rhnrt questions.
(ill[(5) Consider Llle following four graphs:
(1) 9
(iv) 3
[a3] 'Which are the graph of a. function? (i) cfw_ii [iii] (iv) (Just
MATH 127 - Final Examination. Fall Term 2009 Page 6 of 10
5. Applications of the derivative.
[3] (3.) Use the linear approiu'mation to nd an approximate value of @
[10] (h) A cylindrical can with height h. and radius 1" is to be used to store coconut milk
MATH 127 : Worksheet 4
Worksheet 4: This worksheet covers sections 3.10, 4.1, 4.3, 4.4, 4.5, 4.7, and 4.8 of the
textbook, which are the pertinent sections for Quiz 4.
1. Use a linear approximation to show that
1
1
x
1+x
near the point x = 0.
2. A pool of
UNIVERSITY OF WATERLOO FINAL EXAM FALL TERM 2009
Student Name (Print Legibly) (family name) Signature Student ID Number (given name)
COURSE NUMBER COURSE TITLE COURSE SECTION(s) DATE OF EXAM TIME PERIOD DURATION OF EXAM NUMBER OF EXAM PAGES (Including thi
MATH 127 Fall 2013
Assignment 10
Topics: Substitution rule, approximate integration, and area between curves
Due: 12:00 pm, Wednesday, November 27th
1. Evaluate the following
1
dx
+ 2x + 2
(x + 2) 3 xdx
(a)
x2
(b)
1
cos x
dx
x2
(c)
6
(d)
0
1
(e)
0
tan (x)
MATH 127 Fall 2013
Assignment 11
Topics: Volumes of revolution
NOT FOR SUBMISSION
1. Find the volume of the object formed by:
(a) Revolving the region in the rst quadrant bounded by y = ex and its tangent line
at x = 1 about the x-axis.
(b) Revolving the
UNIVERSITY OF WATERLOO FINAL EXAM FALL TERM 2008
Student Name (Print Legibly) (family name) Signature Student ID Number (given name)
COURSE NUMBER COURSE TITLE COURSE SECTION(s) DATE OF EXAM TIME PERIOD DURATION OF EXAM NUMBER OF EXAM PAGES (Including thi
Math 127 Winter 2016
Assignment #8: Exponential Growth/Decay, Differential
Equations, Slope Fields and Eulers Method
Due Monday, March 21st at noon in the drop boxes outside MC 4066
Instructions:
Print your name and I.D. number at the top of the first pag
Math 127 Winter 2016
Assignment #7: Linear Approximation, Newtons Method,
Taylor Polynomials
Due Monday, March 14th at noon in the drop boxes outside MC 4066
Instructions:
Print your name and I.D. number at the top of the first page of your solutions.
Und