PRECALCULUS 114 DAY 5
Name: _
Page |1
Date: _
4.1: POLYNOMIAL FUNCTIONS
A. DEFINITION
A polynomial function P is given by
P( x) an x n an1 x n1 an2 x n2
a1 x a0 ,
where the coefficients an , an 1 ,., a1 , a0 are real numbers and the exponents are whole
PRECALCULUS 114 DAY 3
Name: _
Page |1
Date: _
2.4: LIBRARY OF FUNCTIONS
B.
PIECEWISE-DEFINED FUNCTIONS
A piecewise defined function is a function which is defined symbolically using two or more formulas.
Prof. B. Patiak
PRECALCULUS 114 DAY 3
Page |2
EXERC
PRECALCULUS 114 DAY 2
Name: _
Page |1
Date: _
2.1: FUNCTIONS
I.
DEFINITION OF FUNCTION
B.
A function is a rule of correspondence the associates a value x from the first set to a unique value y from
the second set
REPRESENTING FUNCTIONS
Prof. B. Patiak
PRE
PRECALCULUS 114 DAY 4
Name: _
Page |1
Date: _
3.2: QUADRATIC FUNCTIONS
A. DEFINITION
A quadratic function is a function of the form f ( x) ax 2 bx c , where a, b and c are real numbers
and a 0 . The domain of a quadratic function consists of all real numb
PRECALCULUS 114 DAY 1
Name: _
Page |1
Date: _
1.1: DISTANCE AND MIDPOINT FORMULAS
I.
DISTANCE AND MIDPOINT FORMULAS
Given P1 (x1, y1 ) and P2 (x2, y2 ) , then the distance between the points is given by:
dP1P2 =
( x2 - x1 ) + ( y2 - y1 )
2
2
And the midpo
PRECALCULUS 114 DAY 7
Name: _
Page |1
Date: _
4.4: RATIONAL INEQUALITIES
A. SOLVING RATIONAL INEQUALITIES
Steps:
1) Set the right side of the inequality to 0.
2) Factor both numerator and denominator, if factorable.
3) Find the zeros of the numerator and
PRECALCULUS 114 DAY 6
Name: _
Page |1
Date: _
4.2 4.3: RATIONAL FUNCTIONS
A. BASIC RATIONAL FUNCTIONS
B. DEFINITION
A rational function is a function written as a quotient of two polynomial functions, that is:
R( x)
f ( x)
, g ( x) 0
g ( x)
where f ( x),
PRECALCULUS 114 DAY 8
Name: _
Page |1
Date: _
5.3: SOLVING EXPONENTIAL EQUATIONS
A. SOLVING EXPONENTIAL EQUATIONS
Theorem:
If () = () then ( ) = ()
Steps:
1.
Rewrite the equation using a common base.
2.
Apply properties of exponents to combine the equatio
Rutgers Business School
Fall 2017
Introduction to Probability: Solutions to Homework 1
Problem 1.
The probability pn that in a room of n people they all have different birthdays is
364
363
362
365 n + 1
pn =
.
,
365
365
365
365
for n = 1, 2, . . . , 365.
Math 640:135/CALCULUS I/ Quiz 4/Version 3. - February 12, 2010
Circle one: Section 01 / 02 / 03 / 04 / 05 . Please print:
,
last name
first name
Show all work to receive credit. Please print clearly!. Calculators may not be used.
1. Find Dx y if
(3 points
Math 640:135/CALCULUS I/ Quiz 8/Version 1. - March 26, 2010
Circle one: Section 01 / 02 / 03 / 04 / 05 . Please print:
,
last name
first name
Show all work to receive credit. Please print clearly!. Calculators may not be used.
1. Find the general antideri
Math 640:135/CALCULUS I/ Quiz 10/Version 3. - April 9, 2010
Circle one: Section 01 / 02 / 03 / 04 / 05 . Please print:
,
last name
first name
Show all work to receive credit. Please print clearly!. Calculators may not be used.
1. Find the average value of
Math 640:135/CALCULUS I/Dr. Sturm/ Quiz 2/Version 3. - January 29, 2010
Circle one: Section 01 / 02 / 03 / 04 / 05 . Please print:
,
last name
first name
Show all work to receive credit. Please print clearly!. Calculators may not be used.
1. Find the limi
Math 640:135/CALCULUS I/ Quiz 11/Version 3. - April 23, 2010
Circle one: Section 01 / 02 / 03 / 04 / 05 . Please print:
,
last name
first name
Show all work to receive credit. Please print clearly!. Calculators may not be used.
1. Let f (x) = 2x7 + 3x5 +
Math 640:135/CALCULUS I/ Quiz 9/Version 3. - April 2, 2010
Circle one: Section 01 / 02 / 03 / 04 / 05 . Please print:
,
last name
first name
Show all work to receive credit. Please print clearly!. Calculators may not be used.
1. Find G0 (x) in each of the
2. Let f (x) = x3 + 6x2 + 9x + 4:
(4 points)
a) Determine where the function is increasing.
b) Determine where the function is decreasing.
c) Determine where the function is concave up.
d) Determine where the function is concave down.
3. Let f (x) = x2 +
Math 640:135/CALCULUS I/ Quiz 3/Version 3. - February 5, 2010
Circle one: Section 01 / 02 / 03 / 04 / 05 . Please print:
,
last name
first name
Show all work to receive credit. Please print clearly!. Calculators may not be used.
1. Use f (x) = limh0 [f (x
Math 640:135/CALCULUS I/ Quiz 1/Version 2. - January 22, 2010
Circle one: Section 01 / 02 / 03 / 04 / 05 . Please print:
,
last name
first name
Show all work to receive credit. Please print clearly!. Calculators may not be used.
Do not simplify your answe
Math 640:135/CALCULUS I/ Quiz 5/Version 3. - February 19, 2010
Circle one: Section 01 / 02 / 03 / 04 / 05 . Please print:
,
last name
first name
Show all work to receive credit. Please print clearly!. Calculators may not be used.
1. An object is moving al
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Practice Test #1 Problem Solving
(196 Questions)
1.
409-!-item-!-187;#058&000306
A grocery store purchased crates of 40 oranges each for $5.00 per crate and then sold each
orange for $0.20. What was the store's gross profit on each crate of oranges?
(A) $
Practice Test #2 Problem Solving
(197 Questions)
1.
246-!-item-!-187;#058&000117
Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she
prepared an envelope with its correct address. If the 4 letters are to be put int
CrackVerbal Quant Question Bank
1) If (1/5)m(1/4)18 = 1/2(10)35, m?
2) (-1)k+1(k). T is the sum of the first 10 k, is t
a. > 2
b. between 1 and 2
c. between and 1
d. between and
e. <
3) What is m+n?
+
4
e
f
x
1
7
2
Y
-5
N
-4
z
m
10
5
4) Perimeter of iso
Geometry Formula:
Triangle
Pythagorean Theorem
30.60.90 degree phenomenon
30-60-90 degree phenomenon
Combinations: (3-4-5), (5-12-13), (8-15-17),
(6-8-10), ( 9-12-15), (12-16-20), (10-24-26)
Perimeter of Triangle
Area of any Triangle
Area of Isosceles Tri
Author
Message
(7) Besides Complex roots, even irrational roots occur in pairs. Hence if 2+root(3) is a root, then even 2-root(3) is a root . (All these are very
useful in finding number of positive, negative, real, complex etc roots of an equation )
(8)
. Exam # 2 Math 327-02 Probability & Statistics Fall 2016
Name (print) was_
On my honor, I have neither received nor given any unauthorized assistance on this examination.
Signed,
INSTRUCTIONS: Show all of your work for maximum credit. The point value of
REVIEW # 3
21:640:327
PROBABILITY & STATISTICS
FALL2016
You may bring in two pieces of 8.5 x 11 paper with anything you want written on
both sides of them. You must print your name on these papers and turn them in with
your exam paper. Calculators may be
PROBABILITY HOMEWORK ANSWER KEY
1) D -0.23. The probability of an event must be between 0 and 1, inclusive, so we cannot have
negative probabilities.
2)
3
1
a) (red) = 12 = 4 = 0.25
b) (red or white) =
c) (not white) =
3)
3+4
3+5
12
12
7
= 12
8
2
= 12 = 3
Page | 1
Hassan Ouanir
Abstract
With the study of prime numbers in number theory comes the question of how prime
numbers are distributed. This is a central question in Analytic number theory. The distribution of
prime numbers is a question about how often
HW 8-Courtney Washington https:/x1itemprod.pearsoncmg.com/api/vl/print/math
Student: Courtney Washington Instructor: Jacob Sturrn Assignment: HW 8
Date: 5311? Course: Math 119:16 Spring 2017
1. Evaluate the following integrals.
4 7
"' 2 6
(a) Ixs dx (b)