Bcalc Defs

Front 1

approaches

Back 1

let u be a variable quantity (function value or individual variable) and b be a real number
u app b
u app b-
u app b+
u app -inf
u app +inf

Front 2

u app b

Back 2

if the distance between u and b eventually remains less than every given positive distance

Front 3

u app b-

Back 3

if u approaches b and u<b

Front 4

u app b+

Back 4

if u approaches b and u>b

Front 5

u app -inf

Back 5

if u eventually remains less than every given real numb

Front 6

u app +inf

Back 6

if u eventually remains more than every given real number

Front 7

composition

Back 7

f=g if (1) f&g have the same domain (2) f(a)= g(a) for every a in the domain

Front 8

continuous

Back 8

a function f is continuous at c if
(a) f is defined at c
(b) lim f(x) exists, and
x->c
(c) lim f(c)
x->c

Front 9

greater than

Back 9

a number a is greater than a number b if the difference a-b is positive

Front 10

limit

Back 10

let f be a function and c be either a real number, the symbol (+inf), or the symbol (-inf)

Finite limit: a real number L is a limit of f at c if f(x) approaches L as x approaches, but does not equal, c

Infinite lmite: the limit of a function is infinite if either f(x)-> -inf or f(x)-> +inf as x approaches c