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The slope of a line through the points

# The slope of a line through the points - A little bit of an...

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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 3-51 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 +(1-x)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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Linear functions have y for which all x is defined, constant functions have 0 slope and same y throughout, undefined non-functions 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… y-intercept is determined by: f(0)=mx + b: m(0)+b, whereas x-intercept 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 cost-benefit models, and exclude all values for zero in denominator
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The slope of a line through the points - A little bit of an...

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