Mathematics 115 F2013 / Exam 4 Some Practice Problems
(1) Find each of the following denite and indenite integrals; one part of one of the following cannot
be solved - which one?
ex ex
dx
ex + ex
(a)
-Review of pre-calculus before we start working on calculus
I. The concept of the function is the most fundamental to calculus.
a. Functions model real life systems
b. The simplest function is a const
I. Rational Functions
a. The quotient of two polynomials is a rational function.
b. The domain of a rational function is all x except where f(x) = 0.
c. Wolfram Alpha is an online app for checking gra
I. Quiz 1 Tuesday: Topics
a. Trig
b. Limits
c. No calculators
II. Limits
a. A function f(x) has limit L as x approaches a.
a.i. Denoted limx approaches a f(x) = L
a.ii. If all values of f(x) are close
I. Polynomial Functions
a. A quadriatic function f is given by f(x) = ax2 +bx +c, where a does not
equal 0.
b. The vertex of a parabola is given by the equation x = -b/2a.
b.i. Once one finds the x co
I. Slope and Linear Functions
a. The definition of calculus evolves as an individuals knowledge of the
subject grows.
b. Y=mx+b is called the slope intercept equation of a line.
c. A constant function
MATH 115 000/001 LIFE SCIENCES CALCULUS 1
SYLLABUS FALL 2012
Following are an overview of the course and a detailed week-by-week syllabus with
exam and quiz dates. Please note that this syllabus is te
I. Trigonometric Functions
a. A positive angle is counterclockwise.
b. A negative angle is clockwise.
c. The rotating ray is called the terminal side of the angle while the positive
side of the x-axis
I. 2.1 Limits and Continuity: Numerically and Graphically
a. Absolute zero is the limit scientists approach as they develop more
advanced cooling methods. This limit cannot be reached.
b. In order for
I. 2.2 Limits: Algebraically
a. Limit Principles (let c be a constant and suppose that lim of f(x) is L and
lim of g(x) is M as x approaches a.
a.i. Lim cf(x) = cL as x approaches a.
a.ii. Lim (f(x)+g
Mathematics 115 F2011 - Example Problem
Let f (x) =
x.
(1) Use the denition of the derivative to nd f (x):
From the denition
f ( x + h) f ( x )
f (x) = lim
= lim
h 0
h 0
h
x+h
h
x
provided the limit e
Maria Agnesi: (May 16, 1718 - January 9, 1799)
Born in Milan
Age 5- spoke French and Italian
Age 9- gave an academic speech about womens rights on education
Age 10- spoke 7 languages
Wrote book on dif
Math 115 - Exam 1 - Sample Problems - Fall 2013
Here are some sample problems to give you an idea of the type of problems that will appear on
Exam 1. Some of the problems are a bit long for an exam bu
Mathematics 115 F2013 / Exam 2 Some Practice Problems
(1) Find the derivatives of each of the following functions. Show all steps, reasoning and calculations. Name the main dierentiation rules used.
(
Math 115 Solutions to Exam 4 Practice Problems Fall 2013
The following solutions are not complete answers in call cases; there is enough here for you to start
your solutions and to check your nal answ
Mathematics 115 F2013 / Exam 3 Some Practice Problems
(1) #22, p. 235 is a typical max-min problem.
(2) #26, p. 235 is a very good max-min problem.
(3) #34, p. 254 is a typical related rate problem.
(
Mathematics 115 F2013 / Exam 5 Some Practice Problems
(1) Solve the higher-order initial-value problem: f (x) = 2x; f (1) = 2 and f (0) = 1
(2) Do Problems #35, #36 on p. 550 and add one more part for
my,
again-y-
. (15pts)
Consider the two functions
f(:c)=as2+x+3 g(:c)=3a:+2
(i) Find the value a: = b Where the two functions intersect.
(ii) Compute the area of the region enclosed by the graph
Mathematics 115 Fall 2013: Practice Problems for the Final Examination
When doing these practice problems, write out complete careful solutions, including all work,
calculations and reasoning. It help
Mathematics 115 Fall 2011
Max/Min, Exponential Growth/Decay
Heating/Cooling, and Limited Growth Problems
When answering these questions, make sure to show all work and reasoning, and use the correct
u
Math 115 / Fall 2011
Math 115 Life Science Calculus 1 Precalculus Review Fall 2011
The following exercises review the basic functions we will use in this course.
(A) Basic properties of functions, com
Mathematics 115 Fall 2011: A Comprehensive Example
Please note: You should try to do the following problem before you read the solution. It requires accurate
sketches of two graphs, nding points of in
Mathematics 115 F2011: Syllabus for Exam 1
A. The best ways to prepare for the test are to:
read your notes from the lectures and labs;
read all the sections listed below, being careful to do as man
Math 115 / Fall 2011
Math 115 Life Science Calculus 1 Precalculus Review Fall 2011
The following exercises review the basic functions we will use in this course.
(A) Basic properties of functions, com