Download hw1 due - EOU Physics

Math 251- Calc I
Homework #1
Dr. Tovar
Book: Essential Calculus by Stewart
Trigonometry
1)
If a symmetric hexagon has sides of length a, what is the area of the hexagon. (Show your
work.)
2)
Explain how a construction worker can insure that a corner is “square” by using a Pythagorean
Triplet.
3)
In Dr. Tovar's Trigonometry Tutorial there is a list of Pythagorean Triplets, the last of which is
2
13 + 842 = 852. Determine the next Pythagorean Triplet which starts with 142 + ... (Hint: if you can't
figure it out, the answer is in the tutorial, read it!)
4)
In trigonometry, we base our triangles off of the unit circle. This leads to something absolutely
weird and unusual. What is it?
5)
In your own words, define each of the following: (You may get help from ANY source!)
Types of Functions:
single-valued function
multi-valued function
continuous function
domain of a function
range of a function
1-1 function
monotonic increasing function
monotonic decreasing function
vertical line test
horizontal line test
piecewise defined function
positive definite function
positive semi-definite function
negative definite function
negative semi-definite function
symmetric function
odd function
even function
inverse function
periodic function
Math 251- Calc I
Homework #2
Dr. Tovar
Book: Essential Calculus by Stewart
1)
In your own words, define each of the following: (You may get help from ANY source!)
Properties of Functions:
asymptote
critical values
extremum
slope
tangent line
normal line
concave up
concave down
inflection point
independent variable
dependent variable
single-variable
multi-variable
arc length
local minimum
local maximum
absolute minimum
absolute maximum
x-intercept
y-intercept
fixed points
bounded
unbounded
Specific Functions:
elementary functions
rational functions
pulse functions
Heaviside step function
signum function
Equations:
explicit equation
implicit equation
parametric equations
Number Systems:
countable infinity
uncountable infinity
natural numbers
whole numbers
integers
real numbers
complex numbers
extended real number system
Graphs:
abscissa
ordinate
quadrant
2)
Fill in the table below:
As before, you may use any source. However, keep in mind that the goal is to actually learn the
symbols. (Hint: Many of the answers are at
http://en.wikipedia.org/wiki/Table_of_mathematical_symbols )
Symbols:
Symbol
Meaning
there exists
For all
Ʃ
Summation
Π
Product
Proportional to
Therefore
Because
±
Plus or Minus
Minus or Plus
Implies
If and only if
Defines
Approximately
Infinity
()
Open interval
[]
Closed interval
(]
Left open interval
[)
Right open interval
Perpendicular
Set of Integers
Set of Rational Numbers
Set of Real Numbers
Set of Complex Numbers