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
1
MATH 127 : Calculus 1 for the Sciences
Weekly Online Assignment #6: Properties of the Derivative
Due by 9:00 pm on WEDNESDAY, June 7, 2017
Weight: 2%
Instructions:
Ensure you have completed the weekly tasks up to and including Friday, Week 5, on Rules
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
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 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
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
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
Math 127 Final Exam Syllabus
Be able to:
Work with trigonometric, inverse trigonometric, exponential, logarithmic, and algebraic
functions.
Determine limits, possibly using LHospitals Rule: as x tends to a real number or as x tends to
infinity.
Find the d
Unit 1 Introduction to the Cell
historicai
light microscopy and the discovery of the cell, cell theory
facts, hypotheses, theories and the scientific method
strands of cell biology cytology, biochemistry, genetics
basic properties of cells
classes of cell
Lecture 5
Proposition 5.1 (Bounds by Divisibility (BBD). Let a and b be integers. If a | b and
b 6= 0 then |a| |b|.
Proof. Let a, b be integers and assume that a | b and b 6= 0. Since a | b, there exists an integer
q so that b = qa. Since b 6= 0, q 6= 0.
Combining Functions
Given a function with domain and a function with domain we can
construct
.a new
function
defined by
and whose domain consists of all that
satisfy
and .
and .
and .
, , and .
and .
Definition of a Composite Function
Given
two functions
For those left flustered by our necessarily cursory first look at sequence notation, I hope this
clears things up.
Here again are some examples of sequences: quantum energy levels, measurements (of
anything!) taken at discrete time points, the intensities
Addendum to Supporting Material for Lecture 1.2
Example: A sealed chamber is filled with a fixed amount (in moles) of an ideal gas. Using a
piston, the volume of gas is gradually decreased under isothermal (constant temperature)
conditions. The volume at
Supporting Material for Lecture 1.2
Given a function with domain and a function with domain , we can construct
.a new function
=+
=
=
= /
=
defined by
() = () + ()
() = () ()
() = ()()
() = ()/()
() = ()
and whose domain consists of all that satisfy
1
MATH 127 : Calculus 1 for the Sciences
Weekly Online Assignment #10:
Applications of Differentiation and Introduction to Integration
Due by 9:00 pm on WEDNESDAY, July 5, 2017
Weight: 2%
Instructions:
Ensure you have completed the weekly tasks up to and
Review Problem Set 1
1. (a) Solve:
(b) Solve for 0 x < 2:
(i) |x| x2 = 2x + 1
(ii) |2x + 1| 5
(i) |2 cos x 1| < 1
(ii) 4 sin 2x + cos x csc2 x = 0
2. Find the equation of the tangent line to the curve arcsin(xy) =
3. Evaluate the following integrals:
Z 2