Foundations of Accounting (ACC 310F)
Assignment 4
Part A
A1. The Williams Company had the following accounting framework available:
Required:
a. If $240 of insurance expired, what dollar amount of end
Integration Worksheet - Substitution Method Solutions
The following are solutions to the Math 229 Integration Worksheet - Substitution Method. Heres
the link to that worksheet http:/www.math.niu.edu/c
Summative Assessment
tech n ical B u lleti n #1
Version 3, August 2014
actaspire.org
ACT endorses the Code of Fair Testing Practices in Education and the Code of Professional Responsibilities in
Educa
Integration
by substitution
There are occasions when it is possible to perform an apparently difficult piece of integration
by first making a substitution. This has the effect of changing the variable
AP CalculusIntegration Practice
I. Integration by substitition.
Basic Idea: If u = f (x), then du = f 0 (x)dx.
Example. We have
Z
x dx
x4 + 1
u = x2
=
dx = 2x dx
=
=
1
2
Z
du
+1
u2
1
tan1 u + C
2
1
ta
Integration By Partial Fractions
Objectives
Understand the Concept of a Partial Fractions Decomposition
Use Partial Fractions Decomposition with Linear Factors to Integrate
a Rational Function
Use
Partial fractions
3.6
Introduction
It is often helpful to break down a complicated algebraic fraction into a sum of simpler fractions.
1
3
For example it can be shown that x24x+7
has the same value as
Question1 2 pts
If a bank was trying to determine whether our company should be issued a longterm loan, it would most likely use which of the following ratios?
Currentratio
Daysinaccountsreceivable
SOLUTIONS TO EXAM 1, MATH 10560
Problem 1. Evaluate the integral
Z
2
2
dx
.
4 + x2
Solution.
Z
2
2
Now put u =
x
2
1
dx =
4 + x2
Z
2
2
1
4 1+
1
dx =
x2
4
4
Z
2
2
1
2 dx.
1 + x4
then dx = 2du. Also x
Table of Useful Integrals, etc.
e
ax 2
0
1
dx =
2 a
2 ax 2
x e
0
0
n ax
xe
dx =
0
ax 2
dx =
0
1
2
3 ax 2
x e
dx =
0
(
)
1 3 5 2n 1
dx =
a
2 n+1 a n
x e
2
1
dx =
4a a
2n ax 2
x e
1
1
2
2
1
2
Partial Fractions
A rational function is a fraction in which both the numerator and denominator are polynomials.
x + 26
4
3
For example, f ( x) =
, g( x) =
, and h( x) =
are rational functions. You
2
LH
opitals rule practice problems
21-121: Integration and Differential Equations
Find the following limits. You may use LHopitals rule where appropriate. Be aware that LHopitals
rule may not apply to
1.3
Sum of discrete random variables
Let X and Y represent independent Bernoulli distributed random variables
B(p).
Find the distribution of their sum
Let Z = X + Y . The probability P (Z = z) for a
1
Probability
1.1
Normal distribution
The hemoglobin values of an undoped athlete1 are known to be normally
distributed with = 148 and variance 2 = 85. Let X denote a measured
value of hemoglobin, i.e
1.6
The distribution of the average
As another example from the doping case, we now consider the mean value
of each individual. As it turns out, each individual may have his own mean
value and these v
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Mathematical Techniques : Differentiation SAMPLE
The total number of marks is 30. The marks available for each question are indicated in
parentheses. The pass mark is 24 or above. 1 alculators must
Math 273
Practice problems for exam 2
1. Evaluate each double integral:
a)
Z 2Z
0
4x
(x2 + y) dy dx
b)
x
Z
2
0
Z
Z 2 Z 4y2
cos(x2 + y 2 ) dx dy
c)
3
r2 sin() dr d
0
0
0
2. For each part of #1, sketch
DIFFERENTIATING UNDER THE INTEGRAL SIGN
KEITH CONRAD
I had learned to do integrals by various methods shown in a book that my high
school physics teacher Mr. Bader had given me. [It] showed how to dif
MATHEMATICS IA CALCULUS
TECHNIQUES OF INTEGRATION
WORKED EXAMPLES
Find the following integrals:
Z
1.
3x2 2x + 4 dx. See worked example Page 2.
Z
2.
Z
3.
Z
4.
Z
5.
Z
6.
Z
7.
Z
8.
Z
9.
Z
1
1
dx. See wor
Double integrals
Notice: this material must not be used as a substitute for attending
the lectures
1
0.1
What is a double integral?
Recall that a single integral is something of the form
Z b
f (x) dx
5
Indefinite integral
The most of the mathematical operations have inverse operations: the
inverse operation of addition is subtraction, the inverse operation of multiplication is division, the invers
Lecture Notes
Integrating by Parts
page 1
Sample Problems
Compute each of the following integrals. Please note that arcsin x is the same as sin
as tan 1 x
1.
Z
xex
dx
2.
Z
x cos x dx
3.
Z
4.
Z
xe
4x
d
The Literacy and Numeracy Secretariat
The Capacity Building Series is
produced by The Literacy and
Numeracy Secretariat to support
leadership and instructional
effectiveness in Ontario schools.
The se
TJs Study Guide for Math 212
The best way to feel confident for the exam is to know your stuff cold. What
do I mean by that? Most concepts and mathematical objects weve learned
about have several face