ap calc formulas

slope intercept form

y = mx + b

point slope form

y - y1 = m(x - x1)

standard form of line

Ax + By = C

rate of change (1)

change in y / change in x

rate of change (2)

(y1 - y2)/(x1 - x2)

rate of change (3)

[f(a) - f(b)] / (a - b)

quadratic standard form

ax² + bx + c

quadratic formula

-b/2a +- sqrt(b²-4ac)/2a

sphere volume

V = 4/3 pi r³

sphere SA

SA = 4 pi r²

cone volume

V = 1/3 pi r²

trapezoid area

A = 1/2(h)(b1 + b2)

triangle area

A = 1/2(b)(h)

area of box

(l)(w)(h)

surface area of box

2(l)(w) + 2(l)(h) + 2(h)(w)

right triangle sin

opp/hyp

right triangle cos

adj/hyp

right tri tan

opp/adj

circ func sin

y/r

circ func cos

x/r

circ func tan

y/x

recip func csc

1/sin theta

recip func sec

1/cos theta

recip func cot

cos theta/sin theta, 1/tan theta

recip func, 1 = (1)

sin x csc x

recip func, 1 = (2)

cos x sec x

recip func, 1 = (3)

tan x cot x

pythag, 1 =

sin²x + cox²x

pythag, sec²=

1 + tan²x

pythag, csc²x=

1 + cot²x

lim sin x as x approaches c

sin c

lim cos x as x approaches c

cos c

f(x) continuous at point (c, f(c)) if (1)

f(c) exists

f(x) continuous at point (c, f(c)) if (2)

lim f(x) as x approaches c exists

f(x) continuous at point (c, f(c)) if (3)

lim f(x) as x approaches c = f(c)

even function (1)

sym w respect to y-axis

even function (2)

f(x) = -f(x)

odd func (1)

sym w respect to origin

odd func (2)

f(-x) = -f(x)

lim (sin x)/x as x approaches 0

1

lim (1-cos x)/x as x approaches 0

0

domain of sqrt[s(x)]

s(x) greater than or equal to 0

domain of 1/s(x)

s(x) not equal to 0

domain of ln(s(x))

s(x) greater than 0

lim f(x) as x approaches a exists if

lim f(x) as x approaches a from left = lim f(x) as x approaches a from right

cos pi/2, sin pi/2, tan pi/2

0, 1, undefined

cos pi/3, sin pi/3, tan pi/3

1/2, sqrt(3)/2, sqrt(3)

cos pi/4, sin pi/4, tan pi/4

sqrt(2)/2, sqrt(2)/2, 1

cos pi/6, sin pi/6, tan pi/6

sqrt(3)/2, 1/2, sqrt(3)/3

cos 0, sin 0, tan 0

1, 0, 0

y = a sin b(theta - c) + d

y = a cos b(theta - c) +d

a = amplitude, 2pi/b = pd, phase shift = c, vert shift = d

y = a tan b(theta - c) + d

abs val (a) = vert stretch, pi/b = pd, phase shift = c, vert shift = d

a³+b³

(a+b)(a²-ab+b²)

a³-b³

(a-b)(a²+ab+b²)

a²-b²

(a+b)(a-b)

(a+b)³

a³+3a²+3ab²+b³

(a-b)³

a³-3a²+3ab²-b³

(a+b)²

a²+2ab+b²

(a-b)²

a²-2ab+b²

double angle

sin 2 theta = 2 sin theta cos theta

cos 2 theta = cos²theta - sin²theta or 2cos²theta-1

sin (u +- v)

sin u cos v +- cos u sin v

cos (u +- v)

cos u cos v +- sin u sin v

def of derivative f(x) at (x, f(x))

lim as change x approaches 0 = [f(x + change x)-f(x)]/change x

derivative of f(x) at (c, f(c)) at specific point

lim as x approaches c = [f(x)-f(c)]/x-c

d/dx u^n

nu^n-1 (u’)

slope of curve at a point

= slope of the line tangent to the curve at that point

s’’(t) = v’(t) = a(t)

acceleration function

s’(t) = v(t) = f a(t)dt

velocity function

s(t) = f v(t)

position function

d/dx [uv]

u’v+v’u

d/dx [u/v]

(u’v - v’u)/v²

d/dx [u+-v]

u’ +- v’

d/dx [ln u]

u’/u = u’(1/u)

d/dx [e^u]

e^u u’

d/dx [log a u]

u’ / (ln a)u

d/dx [a^u]

(ln a)a^u u’

d/dx [sin u]

cos u u’

d/dx [cos u]

-sin u u’

d/dx [tan u]

sec²u u’

d/dx [cot u]

-csc²u u’

d/dx [sec u]

sec u tan u u’

d/dx [csc u]

-csc u cot u u’

find HA

m greater than n, no HA

m less than n, HA is y = 0

m = n, HA is y = a/b

polar to rectangular

x = r cos theta

y = r sin theta

rectangular to polar

theta = tan^-1 (y/x)

r = sqrt(x²+y²)

trig form of complex num

z = r(cos theta + i sin theta)

z = r cis theta

d/dx [arc sin u]

u’ / sqrt(1-u²), u not equal to 1

d/dx [arc cos u]

-u’ / sqrt(1-u²), u not equal to +-1

d/dx [arc tan u]

u’ / 1 + u²

d/dx [arc cot u]

-u’ / 1 + u²

d/dx [arc sec u]

u’ / abs val(u) sqrt(u² - 1), u not equal to +- 1, 0

d/dx [arc csc u]

-u’ / abs val(u) sqrt(u²-1), u not equal to +- 1, 0

(f^-1 (x))’ =

1/f’(f^-1(x)) = 1/(f’ o f^-1)(x)