Math 1426
Midterm 1 Version A
Spring 2013
with solutions
Print your name legibly as it appears on the class rolls:
Last _ First _
ID Number: 1 0 0 0 _ _ _ _ _ _
Check the appropriate section:
100 Dr. Krueger
110 Dr. Krueger (ESP)
200 Ms. Rangel
300 Dr. Ya
Math 1426
Midterm 1 (Version A)
Print your name legibly as it appears on your class roll.
Last
First
ID Number:
Check the appropriate section:
100 - Ms. Ray (MoWeFr 8:00AM - 8:50AM)
200 - Dr. Krueger (MoWeFr 9:00AM - 9:50AM)
300 - Ms. Rangel (MoWe 4:00PM
Math 1426
Midterm 2 Version A
Spring 2011
with solutions
Print your name legibly as it appears on the class rolls:
Last _ First _
ID Number: 1 0 0 0 _ _ _ _ _ _
Check the appropriate section:
001 Dr. Krueger
002 Dr. Krueger (ESP)
003 Ms. Beck
004 Mr. Teng
Math 2425
7.3 Trigonometric Integrals
Calculus II
Integrating Trigonometric Functions
Ex: Solve the indefinite integral. (Notice how the power for sine is odd.)
sin3 () cos4()
Page 1 of 4
Math 2425
7.3 Trigonometric Integrals
Calculus II
Ex: Solve the d
Math 2425
8.5 The Ratio, Roots, and Comparison Tests
Calculus II
The Comparison Tests
Theorem: The Comparison Test
Suppose that and are series with positive terms.
If is convergent (resp. divergent) and (resp. ) for all , then is also convergent
(resp. di
Math 2425
8.1-8.2 An Overview of Sequences and Series
Sequences
Examples and Notation
cfw_2, 4, 6, 8, , 2,
1 2 3 4
,
cfw_ , , , , ,
2 3 4 5
+1
3
4
5
6
Ex: Find a formula for the general term an of the sequence, cfw_5 , 25 , 125 , 625 , .
Definition: Sequ
Math 2425
8.6 Alternating Series
Calculus II
Alternating Series
DEFINITION: A series whose adjacent terms alternate between positive and negative values is referred to as an
alternating series.
Theorem: Alternating Series Test
Assume > 0. The alternating
Math 2425
7.8 Improper Integrals
Calculus II
Improper Integrals
The definition of a definite integral requires that the interval of integration, [a, b], be finite. Furthermore, the
Fundamental Theorem of Calculus requires that the integrand be continuous
Math 2425
7.2 Integration by Parts
Calculus II
Integration by Parts
(The product rule for integration)
Integration by Parts
If and are differentiable functions of , then
=
=
Guidelines for Integration by parts
i. Try letting be the more complicated
Math 2425
7.1 Basic Integration Techniques
Basic Integration Techniques
Basic Integration Formulas:
Ex: Compare these three similar integrals and their solution methods.
i.
2
4
+9
Calculus II
Math 2425
ii.
7.1 Basic Integration Techniques
4
+9
2
4 2
iii
Math 2425
8.3 Infinite Series
Calculus II
Infinite Series
Question: Is it possible to add an infinite number of values and obtain a finite result?
DEFINITION: An infinite series is an expression that can be written in the form,
PARTIAL SUMS:
1
=
2
=1
Not
Math 2425
7.5 Partial Fractions
Calculus II
Partial Fractions
1
1
1
The Basic Idea behind Partial Fractions: Solve the integral given 2 5+6 = 3 + 2
1
2
5 + 6
Ex: Distinct Linear Factors- Write the partial fraction decomposition for the given rational fu
Math215 - Statistical Concepts
Franklin University
Math215 - Statistical Concepts
Test One Review Sheet
This Review Sheet should be considered as a guide for your study for testone in Math215. However, it should not be considered as the only source of
stu
Math 2413
Notes 3.1
Section 3.1 Related Rates
Recall:
The Derivative as a Rate of Change
Given y = f (x), the slope of the secant line
f (b) f (a )
ba
gives the average rate of change of y with
respect to x over the interval [a,b].
On the other hand, the
Notes 1.3
Math 2413
Continuity
Observation:
There is a hole on the graph of function f(x) at x = -2. We say this function is NOT continuous at x = -2.
There is a vertical asymptote x= 4. We say this function is NOT continuous at x = 4.
At x = 2, there is
Math 2413
Notes 3.4
Section 3.4 Extreme Values
Definition:
A function f is said to take on a local maximum at c if:
f (c) f ( x) for all x sufficiently close to c.
A function f is said to take on a local minimum at c if:
f (c) f ( x ) for all x sufficient
Math 2413
Section 1.4 Notes
Section 1.4 The Intermediate Value Theorem
Theorem 1.4.1: The Intermediate Value Theorem
If f is a continuous function on the closed interval [a,b], and N is a real number such that
f (a) N f (b) or f (b) N f (a), then there is
Math 2413
Notes 3.2
Section 3.2 The Mean-Value Theorem
Definition: If there is an open interval I containing c in which either f (c) f(x) for all x in I , or f (c) f(x) for
all x in I , then we say that f(c) is a local extreme value of f .
In the former c
Math 2413
Section 1.6 Notes
Section 1.6 Limits of Trigonometric Functions and the Pinching Theorem
Let p >0. Suppose that f (x), g(x) and h(x) are defined in an open interval containing x = c (except possible at x
= c).
If h(x) f (x) g(x) and lim h( x ) L
Math 2413
Notes 3.3
Section 3.3 Increasing and Decreasing Functions
Definition: A function f is said to:
i.
Increase on the interval I if for every two numbers x1, x2 in I,
i. x1 < x2 implies that f ( x1 ) f ( x2 ) ;
ii.
Decrease on the interval I if for
Math 2413
Notes 4.2
Section 4.2 The Exponential Functions
Definition: The function
f ( x) a x where a > 0 and a 1 for all real x
is called the exponential function.
Below you will see the graph of y = ax for four values of the base a. Note that the domain
Math 2413
Notes 2.4
Section 2.4 Implicit Differentiation
A function in the form y = f(x) expresses the dependent variable explicitly in terms of the independent variable
and
The slope of the tangent line to the graph of the function y = f (x) at the point
MATH 1426
FALL 2003
MIDTERM 1 VERSION A
PRINT YOUR NAME AS IT APPEARS ON THE CLASS ROLL LEGIBLY
HERE: _
ID NUMBER: XXX XX - _ _ _ _
CHECK THE APPROPRIATE SECTION:
Dr. Ghandehari
Dr. Lin
Dr. Shan
Dr. Vancliff
Dr. Warren
DO NOT WRITE BELOW THIS LINE
_
Course Syllabus Math 1316
MATHEMATICS FOR ECONOMICS AND BUSINESS ANALYSIS
TTh Fall 2013
INSTRUCTOR: N. Wolff
Office Phone: 817-272-0943
OFFICE: PKH 484
E-Mail: [email protected]
TEXT: Mathematical Applications for the Management, Life, and Social Sciences ; 1
MATH 1316 ASSIGNMENT SHEET
TEXT: Mathematical Applications, !0th Custom UTA Edition, Harshbarger & Reynolds
A Departmental Final is required in this course.
calling 817-272-2617.
The Math Clinic offers one -on-one help, and cost share tutoring is availabl
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