A little bit of, an element of x, t, or whatever variable have you. Sum of all little bits or
elements of variables have you, or integral (whole) of little bits of x. The dx or d of x are differentials of
x. constants begin from beginning of alphabet, whereas variables begin from end of alphabet. Pg. 26…
Dean Swift:
on poetry
rhapsody, usually misquoted
"So, Nat'ralists observe, a Flea
“Hath smaller Fleas that on him prey.
“And these have smaller Fleas to bite ‘em,
“And so proceed
ad infinitum
.”what one fool can do, another can. Ancient Simianproverb
Brief calculus and its applications
Goldstein, Lay, Schneider, Asmar
12
th
edition
Ch. 0
pages 351
Functions:
functions and their graphs
some important functions
the algebra of functions
zeros of functions—the quadratic formula and factoring
exponents and power functions
functions and graphs in applications
There are
rational
and
irrational
numbers. A
function
is a basic quantitative tool for describing
relationships. A function of a variable x is a rule f that assigns to each value of a unique number f(x),
called the value of the function at x; read as f of x. The variable x is called the
independent variable
. The
set of values that the independent variable is allowed to assume is called the
domain
of the function. The
range
of a function is the set of values that the function assumes.
Celcius to Fahrenheit: f(x)=9/5x + 32
Cube law
(because everything is cubed) for a voting model: f(x)= Xcubed/Xcubed +(1x)cubed
Functions have intervals; any combination thereof: (),(],[),[]…
that define a function by separate
formulas…
Y is the
dependent variable
and all functions have one y to one x value(s); one can test this with the
vertical line test…
Acetylcholine (frog heart) when introduced into cardiac tissue diminishes force with which muscles
contract, A.J.Clark… R(x)=100x/b+x where x>_ 0… where x is concentration of ACh, b is positive
constant dependent on particular frog and R(x) muscle response to ACh expressed as percentage of
maximum possible effect of drug…
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View Full DocumentLinear functions have y for which all x is defined, constant functions have 0 slope and same y throughout,
undefined nonfunctions are vertical; violate vertical rule…
Fixed cost: rent, insurance, business loans… costs incurred no matter how many items, products/services
produced… variable costs: depend on number of items produced…
yintercept is determined by: f(0)=mx + b: m(0)+b, whereas xintercept is defined as f(x)=0: mx + b… mx
= b… x=b/m, answer(s) expressed as (0,y) and (x,0) respectively.
piecewise functions
define functions that are expressed by more than one expression…
functions with squares are curvilinear (parabolas)
and are termed quadratic functions: f(x)=axsquared +
bx + c where a is not 0, and domain(s) are all real numbers
polynomia
l domains consist of all numbers. A function expressed as quotient of two polynomials is called
a
rational function
and are used in costbenefit models, and exclude all values for zero in denominator
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 Spring '09
 Calculus, Derivative, Slope, blue box

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