Groundwater Lab Report/ANSWER SHEET
Answer the lab questions for this week and summarize the lab experience using this
form.
Pay special attention to the graphs and figures.
Complete this weeks lab by
QIBT
1201SCE MATHS 1A
Problem & Solutions sheet for week 4
These questions are based the week 3 lectures
Question 1 Practice question on determinants
Calculate the following determinants and check tha
L2-Computation of limits.notebook
August 31, 2014
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L2-Computation of limits.notebook
August 31, 2014
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L2-Computation of limits.notebook
August 31, 2014
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L2-Computation of limits.notebook
August 31,
L1-The concept of limit.notebook
August 31, 2014
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L1-The concept of limit.notebook
August 31, 2014
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L1-The concept of limit.notebook
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L1-The concept of limit.notebook
August 31, 201
4.4 THE DEFINITE INTEGRAL
For any given value of t, the area is given by the limit of the
Riemann sums,
where for each i, ci is taken to be any
point in the subinterval [xi 1, xi].
DEFINITION 4.1
For
4.5 THE FUNDAMENTAL THEOREM OF CALCULUS
THEOREM 5.1 (The Fundamental Theorem of Calculus, Part I)
If f is continuous on [a, b] and F(x) is any anti derivative of f(x),
then
( ) = ( ) ( )
We will ofte
5.2 VOLUME: SLICING, DISKS AND WASHERS
Any solid whose cross sections perpendicular to some axis
running through the solid are all the same. We call any such
solid a cylinder
The volume of a right cir
6.3 TRIGONOMETRIC TECHNIQUES OF INTEGRATION
Integrals Involving Powers of Trigonometric Functions
Consider integrals of the form
Case 1: m or n Is an Odd Positive Integer
1. Evaluate cos4x sinx dx
6.4 INTEGRATION OF RATIONAL FUNCTIONS USING PARTIAL
FRACTIONS
In this section, we introduce a method for rewriting certain rational
functions that is very useful in integration as well as in other
app
CHAPTER 6
Integration Techniques
6.2 INTEGRATION BY PARTS
can not be evaluated with what you presently
know.
INTEGRATION BY PARTS
1.Evaluate x sinxdx
=
A Poor Choice of u and dv
2. Evaluate lnx dx.
5.3 VOLUMES BY CYLINDRICAL SHELLS
In this section, we present an alternative to the method of
washers discussed in section 5.2. Let R denote the region
bounded by the graph of y = f(x) and the x-axis
CHAPTER 5.
Applications of the Definite Integral
5.1 AREA BETWEEN CURVES
1. Find the area bounded by the graphs
of y = 3 x and y = x2 9.
2. Find the area bounded by the graphs of y
= x2 and y = 2 x2 f
4.8 THE NATURAL LOGARITHM AS AN INTEGRAL
DEFINITION 8.1
For x > 0, we define the natural logarithm function, written ln x,
by
=
1
1
Graph of =
THEOREM 8.1
For any real numbers a, b > 0 and any rati
CHAPTER 4
Integration
4.1 ANTI DERIVATIVES
Finding a way to Undo the derivative
1. Find an anti - derivative of () = 2
THEOREM 1.1
Suppose that F and G are both anti - derivatives of f on an
interval
4.6 INTEGRATION BY SUBSTITUTION
1. 2
2
2. ( 3 + 5)100 (3 2 )
INTEGRATION BY SUBSTITUTION
Integration by substitution consists of the following general steps,
as illustrated in example 2.
Choose a ne
3.3 MAXIMUM AND MINIMUM VALUES
For a function f defined on a set S of real numbers and a number c S,
DEFINITION 3.1
(i) f(c) is the absolute maximum of f on S if f(c) f(x) for all x S and
(ii) f(c) is
QIBT 1201SCE , Mathematics 1A,
Solutions for Problem Class 2 Due week 8
Question 1
The range of a function f ( x) = the x values where the function f ( x) is sensibly
defined.
The domain of a function
QIBT
1201SCE Maths 1A
Problem sheet for week 6
Topics:
limits
Question 1.
Find the following limits, if they exist :
(a)
(b)
lim
x 5
x-5 ,
x2 - 25
lim x -22 ,
x
x3
(c)
4
lim 5x - 3x + 5 ,
x x 4 - 2x 2
Problem Class 1 - Solutions
Question 1
In this problem you need to look at the
relative sizes of the vectors and also at
their directions.
(a)
The lines AB and CD are parallel and have the same length
QIBT
1201SCE MATHS 1A
Problem sheet & answers for week 2
All the questions for this week are key questions
Question 1
World cigarette production increased approximately linearly between 1970 and 1990
QIBT
1201SCE MATHS 1A
Problem sheet for week 3
*Question 2 Adding velocities (section 6.2, p 39-41)
In the diagram below a boat starts out traveling on a lake at 30 km/hr at a direction of 30
degrees.
1201SCE/1602SCE Answers for midsemester exam 2005
Question 1 (a) The first few lines of the Pascal triangle are easy to write down. Then use the rule that new entry = value just above + value above an
1201SCE
PROBLEM SHEET WEEK 10 SOLUTIONS.
Students should attempt questions 1(a),(f) and 2.
y = x 4 - 12x 3 + 48x 2 - 64x .
Domain.
All values of x.
Intercepts on the x-axis and the y-axis.
When x = 0,
Griffith University, School of Science 1201SCE Mathematics 1A and 1602SCE Mathematics Midsemester examination, April 2005 Time allowed Reading time Working time 10 minutes 2 hours 30 minutes.
READ THE
Answers for midsemester exam Question 1
(c)
This section will often be answered in a complicated way there are 3 key points The horizontal line test says that y = f ( x) has an inverse function if a h