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