MATH 161: Unit One

f(x)=

x^3

f(x)=

IxI

f(x)=

x^4

f(x)=

√x

f(x)=

1/x

f(x)=

1/x^2

domain for polyomials

(-∞,∞)

domain for fractions

x=0

notation of domain for fractions

(-∞,undefined)U(undefined,∞)

domain for radicals

radicand≥0

notation of domain for radicals

(-∞,undefined radicand] or [undefined radicand,∞)

domain for radicals in the denominator of a fraction

radicand>0

notation for domain for radicals in the denominator of a fraction

(-∞,undefined radicand)U(undefined radicand,∞)

radian and degree conversion

π/180°

addition formula for sin

sin(x+y)=sinxcosy+cosx+siny

addition formula for cos

cos(x+y)=cosxcosy-sinxsiny

addition formula for tan

tan(x+y)=[tanx+tany]/[1-tanxtany]

double angle formula for sin

sin2x=2sinxcosx

double angle formula for cos

cos2x=cos^2x-sin^2x

f(x)=

sinx

f(x)=

cosx

f(x)=

tanx

trig identity of sin and cos = 1

sin^2x+cos^2x=1

definition of a limit (description)

the limit of f(x) as x approaches a, equals L

definition of a limit (formula)

lim f(x) = L

(x–>a)

definition of one-sided limits (left-hand limit)

the limit of f(x) as x approaches a from the left is equal to L

definition of one-sided limits (left-hand limit)

the limit of f(x) as x approaches a from the right is equal to L

the limit of f(x) = L as x–>a [is defined if]

the left and right limits are the same

infinite limits are _

vertical asymptotes

function f is continuous at a number a if (reason 1/3)

f(a) is defined [a is the domain of f]

function f is continuous at a number a if (reason 2/3)

lim f(x) exists [the left and right limits are the same]

function f is continuous at a number a if (reason 3/3)

lim f(x) = f(a)

speed is the _ of distance over time

slope