Math 180, Exam 1, Fall 2007
Problem 1 Solution
1. Find the limit, lim
x1
x2 + 2x 3
.
x2 x
Solution: Upon substituting x = 1 into the function f (x) =
x2 + 2x 3
we nd that
x2 x
x2 + 2x 3
12 + 2(1) 3
0
=
=
2 x
21
x
1
0
which is indeterminate. We can resolve
Math 180, Exam 2, Spring 2011
Problem 1 Solution
1. The graph of a function f (x) is shown below:
e
f
d
A
B
C
D
E
F
G
c
b
g
a
(a) Fill in the table below with the signs of the rst and second derivatives of f on each
of the intervals A, . . . , G.
A
B
C
D
Math 180, Exam 2, Practice Fall 2009
Problem 1 Solution
1. Dierentiate the functions: (do not simplify)
f (x) = x ln(x2 + 1),
f (x) = xe
f (x) = arcsin(2x + 1) = sin1 (3x + 1),
x
f (x) =
e3x
ln x
Solution: For the rst function, we use the Product and Chai
1
Running head: SOCIETY FOR HUMAN RESOURCE MANAGEMENT
Society For Human Resource Management
Prisca Burnett
Florida Institute of Technology
2
Running head: SOCIETY FOR HUMAN RESOURCE MANAGEMENT
The Society for Human Resource Management website is the natio
Grading Rubric - Mini Paper 1: SHRM
Note: This assignment is worth 5% of your overall grade
Content and Development
40% possible
Percentage Earned:
Required: Student provides a brief overview of the contents found at the SHRM website
Required: Paper inclu
COM 2224 Business and Professional Writing
Team Evaluation Not Graded
This assignment is due twice during the semester:
o During Week 4 on Thursday at 11:59 p.m., EST/EDT
o During Week 8 on Thursday at 11:59 p.m., EST/EDT
You must e-mail your assignment t
Grading Rubric - Mini Paper 2: So, whats affirmative action?
Note: This assignment is worth 5% of your overall grade
Content and Development
40% possible
Percentage Earned:
Required: Student has completed a brief analysis of the issue
Required: Discuss th
Grading Rubric - Mini Paper 3: Healthcare Legislation
Note: This assignment is worth 5% of your overall grade
Content and Development
40% possible
Percentage Earned:
Required: Student has completed an analysis of at least two healthcare pieces of legislat
Grading Rubric - Peer-reviewed Journal Article Review
Note: This assignment is worth 20% of your overall grade
Content and Development
50% possible
Percentage Earned:
Required: Student has completed an article review consisting of the following:
- Article
Programming Assignment #2: Grades (30 points)
Program Description:
This assignment will give you practice with parameters, returning values, and interactive programs. Turn in a
Java class named Grades in a file named Grades.java, which will be submitted e
Solved Problems on
Limits and Continuity
Overview of Problems
1
x 3x 2
lim
x 2
x 2
3
lim x 1 x 1
2
x3 x2 x 1
lim
x x 3 3 x 2 5 x 2
4
lim x 2 x 1 x 2 x 1
2
5
7
2
x
2x
lim
2x x 1 x 3 x 1
x 0
lim
2
lim
x 0
2
sin sin x
8
x
6
lim
x 0
x
x 0
9
2
x 2 sin x
x
Antoinette Mutume
1.609km = 1 mile, 65,000 miles = 1.046*10 8 m, 1 inch = 2.54cm
I assume that the average wheel has a diameter of 24 inches this is useful in figuring out
how much distance covered in one revolution, this is equal to the circumference of
Math 180, Exam 2, Fall 2010
Problem 1 Solution
1. Find the following limits.
(a) lim
x0
(b) lim
x0
(c) lim
x
ex 1
sin x
ex
sin x 1
4x3 3x + 8
6x3 + x2 + x 12
Solution:
(a) Upon substituting x = 0 into the function f (x) =
ex 1
we nd that
sin x
ex 1
e0 1
0
Math 180, Exam 2, Spring 2008
Problem 1 Solution
1. Find the derivatives of the following functions: (do not simplify)
(a) f (x) = x2 cos(x + 1)
(b) g(x) = sin(x ln x)
(c) h(x) = tan1 (2x2 + 1)
(d) k(x) = (x + x3 )1776
Solution:
(a) Use the Product Rule a
Math 180, Exam 1, Spring 2009
Problem 1 Solution
1. Evaluate the limits, if they exist:
(a) lim
x1
(b) lim
x3
x+1
x2 + 1
2x2 7x + 3
3x x2
Solution:
x+1
is continuous at x = 1. In fact, f (x) is continuous at all
x2 + 1
x in the interval (, ). Therefore, w
Math 180, Exam 1, Spring 2008
Problem 1 Solution
1. The graph of a function f (x) is shown below.
(a) At which values of x is f discontinuous? Which of these discontinuities are removable?
Which are jump discontinuities?
(b) Determine the limit at each re
Math 180, Exam 1, Fall 2011
Problem 1 Solution
1. Evaluate the following limits. Show your work.
(a) lim
2 cos x
x+12
(b) lim
2x2 + 4x 1
x3 + 1
x0
x+
Solution:
cos x
(a) The function f (x) = 2x+12 is continuous for all x (1, 3) (3, +). Therefore,
since f
Math 180, Exam 1, Fall 2012
Problem 1 Solution
1. Compute the derivatives of the following functions:
x
1 + x3
(b) y = sin( x + 1)
(a) y =
(c) y = x
sin(x) + 1
Solution:
(a) The derivative may be computed using the Quotient Rule.
(1 + x3 )(x) (x)(1 + x3
Math 180, Exam 1, Spring 2010
Problem 1 Solution
1. Evaluate the following limits, or show that they do not exist.
x9
(a) lim
x9
x3
(b) lim
x1
x2 3x + 2
x3 1
(c) lim
x1
|x + 1|
2x + 2
Solution:
x9
(a) When substituting x = 9 into the function f (x) =
we
Math 180, Exam 1, Spring 2011
Problem 1 Solution
1. Evaluate the following limits, or show that they do not exist
x2 + x 6
x2
x2 4
(a) lim
|x2 9|
x3 x2 + 9
(b) lim
(c) lim
x2
x2
x 2
Solution:
(a) Upon substituting x = 2 we nd that
x2 + x 6
22 + 2 6
0
=
=
Math 180, Exam 1, Study Guide
Problem 1 Solution
1. What is the slope of the linear function f (x) whose graph goes through the points (1, 2)
and (4, 4)? What is the value of f (7)?
Solution: The slope of the line that goes through the points (1, 2) and (
Math 180, Exam 1, Practice Fall 2009
Problem 1 Solution
1. Evaluate the following limits, or show they do not exist.
(a) lim 2 cos x
x
x2 4
x2 x + 2
2 x5
(c) lim
x9
x9
(b) lim
Solution:
(a) The function f (x) = 2 cos x is continuous at x = . In fact, f (x
Math 180, Exam 1, Spring 2012
Problem 1 Solution
1. Let c be a real number. Given
(x 1)2 x 3
6 cx
x>3
f (x) =
answer the following questions:
(a) Compute the left hand limit, lim f (x).
x3
(b) Compute the right hand limit, lim f (x).
+
x3
(c) Compute the
Math 180, Exam 1, Spring 2013
Problem 1 Solution
1. Find the value of constant c for which the function given by
cx + 5,
x1
2
x + x 3c, x < 1
f (x) =
is continuous at all points on the real line.
Solution: First we note that cx + 5 and x2 + x 3c are polyn
Math 180, Exam 2, Fall 2008
Problem 1 Solution
1. Find the derivatives of the following functions, do simplify.
(c) arctan(x)
(a) ln(x2 + x + 1),
(b) cos( x),
Solution:
(a) Use the Chain Rule.
[ln(x2 + x + 1)] =
1
(x2 + x + 1)
x2 + x + 1
=
x2
1
(2x + 1)
(it) Even function: reectiona] symmetry
ya.
W
(b) Odd function: rotational symmetry
FIGURE l
FIGURE 2
Periodic function:
translational symmetry
- Guidelines for Sketching a Curve
The following checklist is intended as a guide to sketching a curve 3: = x