What is Calculus?
1. Calculus is the study of advanced algebra and geometry.
2. Calculus is the mathematics of change.
Example 1
1. Calculate the rate of growth of a bacterial culture when dierent variables such as
temperature and food sources are changed
Math 113/114 Midterm Practice Problems
1. Find y . Do not simplify.
x 3
(a) y = (1 3x + e )
(d) y =
tan2 x
1 sec2 x
(g) y = tan(esec
2
(1x3 )
2. Evaluate the limits.
x2 + x 2
(a) lim
x1
x2 1
(e) lim
0
2
(x cos x)
3 x3
2x2 + 1
(b) y =
(e) y = csc2 (x2 sin
MATHEMATICS 113/114
OLD MIDTERM EXAMINATION
VERSION 1
INSTRUCTIONS:
1. Make sure that the exam has ? pages including the cover page.
2. Books, notes, calculators or any other electronic aids are not permitted.
3. Show all your work to receive full credit.
MATHEMATICS 113/114, Final
Examination, V1
Winter 2012
Date: Friday, December 14, 2012
Time: 14:00-16:00
LAST NAME:
FIRST NAME:
(Please, print!)
I.D.:
Please, check your section/instructor!
Course/Section
Instructor
Math 113, Lec G1 Beth Powell
Math 114,
MATHEMATICS 113/114, Final
Examination, V2
Winter 2012
Date: Friday, December 14, 2012
Time: 14:00-16:00
LAST NAME:
FIRST NAME:
(Please, print!)
I.D.:
Please, check your section/instructor!
Course/Section
Instructor
Math 113, Lec G1 Beth Powell
Math 114,
XXX
Math 114-E1 Midterm V2
Oct. 24, 2012
PRINT NAME:
STUDENT ID NUMBER:
1. No books, notes, calculators or cell phones are allowed.
2. Show your work in details.
Problem
Points
1
20
2
20
3
20
4
20
5
20
Total
100
Score
1. (20 pts)
(a) Find the domain of th
XXX
Math 114-E1 Midterm V3
Oct. 24, 2012
PRINT NAME:
STUDENT ID NUMBER:
1. No books, notes, calculators or cell phones are allowed.
2. Show your work in details.
Problem
Points
1
20
2
20
3
20
4
20
5
20
Total
100
Score
1. (20 pts)
(a) Find the domain of th
XXX
Math 114-E1 Midterm V1
Oct. 24, 2012
PRINT NAME:
STUDENT ID NUMBER:
1. No books, notes, calculators or cell phones are allowed.
2. Show your work in details.
Problem
Points
1
20
2
20
3
20
4
20
5
20
Total
100
Score
1. (20 pts)
(a) Find the domain of th
MATHEMATICS 113/114, Final
Examination, V3
Winter 2012
Date: Friday, December 14, 2012
Time: 14:00-16:00
LAST NAME:
FIRST NAME:
(Please, print!)
I.D.:
Please, check your section/instructor!
Course/Section
Instructor
Math 113, Lec G1 Beth Powell
Math 114,
Math 113 (J1) Fall 2010 - Practice Midterm - Solutions
These are the answers only. To receive full marks on the midterm you are required to show
your work.
0
5
10
15
1. The graph of f is
2
1
0
1
2
3
5
3
The domain of f is pV, 1q p1, Vq.
The range of f is
Section 1.2 Combining Functions; Shifting and Scaling Graphs
We will get new functions from the ones we know. Tow functions f and g can be combined
to form new functions by function addition, substraction, multiplication, division and
composition.
(a) Fun
MATH 113/114
Midterm Review Questions
Answer Key
On the midterm show all of your work clearly and make sure that your
nal answer is clearly stated. No calculators, cell phones or formula sheets
will be allowed. This review does not reect the length of you
Math 113/114Solutions to Final Exam Sample Problems
1. Find y .
(a) y = (1 3x2 ) sec2 (x2 1) + (1 x x3 ) 2 sec2 (x2 1) tan(x2 1)(2x).
1
3 sec2 3x
ln(tan(3x) + ln x
x
tan 3x
3 ln x sec2 3x
ln x ln(tan 3x)
y = (tan 3x)
+
x
tan 3x
1
1
(c) y = 3(tan2 x2 sin
Indenite Integrals:
Notation: f (x)dx = Represents a function F(x)+C where F (x) = f (x)
that is it represents a family of antiderivatives of f.
Example 1
1.
2xdx = x2 + C
2.
cos (2x)dx = sin (x) + C
3.
(2x + cos (x)dx = x2 + sin (x) + C
Example 2 Evaluat
MATHEMATICS 113/114
MIDTERM EXAMINATION
VERSION 1
DATE: October 22, 2008
TIME: 50 MINUTES
INSTRUCTIONS:
1. Make sure that the exam has 7 pages including the cover page.
2. Books, notes or calculators are not permitted.
3. Show all your work to receive ful