AP Calculus AB Cheat Sheet

Continuity

1. f(a) exists

2. lim x->a f(x) exists

3. lim x-> a f(x) = f(a)

L'Hopital's Rule

if limx->a f(x)/g(x) = 0/0, then lim x->a f'(x)/g'(x)

IVT

continuous

Derivative Definition

lim h->0 f(x+h)-f(x)/h

d/dx(c)

0

d/dx(cf(x))

cf'(x)

d/dx(x)

1

d/dx(sin(x))

cos(x)

d/dx(cos(x))

-sin(x)

d/dx(tan(x))

sec^2(x)

d/dx(sec(x))

sec(x)tan(x)

d/dx(csc(x))

-csc(x)cot(x)

d/dx(cot(x))

-csc^2(x)

d/dx(sin^-1(x))

1/(sqrt(1-x^2))

d/dx(a^x)

a^xln(a)

d/dxln(x)

1/x x>0

d/dxln|x|

1/x x/=0

d/dxloga(x)

1/(xln(a)) x>0

MVT

1. continuous closed

2. differentiable open

f'(c)=(f(b)-f(a))/(b-a)

inflection points

x = c is an inflection point of f(x) if the concavity changes at x=c

critical points

x =c is a critical point of f(x) provided either f'(c) = 0 or doesn't exist

EVT

1. continuous

2. a <= c, d =

definite integral

int a b f(x)fx = lim n->infinity n/sum/i=1 f(x^*subi) delta x