AP Calc BC - FQ Terms

tan x

sin x/cos x

cot x

cos x/sin x

sec x

1/cos x

csc x

1/ sin x

sin²x + cos²x =

1

sec²x - tan²x

1

sin2x

2sinx cosx

cos2x

cos²x - sin²x

cos²x

½(1 + cos2x)

sin²x

½(1 - cos2x)

sin(-x)

-sinx

cos(-x)

cosx

tan(-x)

-tanx

|x|

x if x >= 0 and -x if x < 0

sin(a+b)

sinAcosB + cosAsinB

sin(a-b)

sinAcosB - cosAsinB

cos(a+b)

cosAcosB - sinAsinB

cos(a-b)

cosAcosB + sinAsinB

sinAcosB

½(sin(A-B) + sin(A+B))

sinAsinB

½(cos(A-B) - cos(A+B))

cosAsinB

½(sin(A+B) - sin(A-B))

cosAcosB

½(cos(A-B)+cos(A+B))

distance formula

sqrt(x2-x1)² + (y2-y1)²

midpoint formula

x1+x2/2 , y1+y2/2

ln(a) + ln(b)

ln(ab)

ln(a) - ln(b)

ln(a/b)

ln(a^n)

n ln a

ln(1/a)

-ln(a)

definition of a limit

LIM = X iff LIM(left) = X = LIM(right)

sin^-1(x) domain & range

D: [-1,1] R: [-pi/2, pi/2]

cos^-1(x) domain & range

D: [-1,1] R [0, pi]

tan^-1(x) domain & range

D: (-inf, inf) R: (-pi/2, pi/2)

lim x→ -inf (e^x)

0

lim x→ inf (e^x)

inf

lim x→ 0+ (lnx)

-inf

lim x → inf (ln x)

inf

lim x→0 ((e^x - 1)/x)

1

lim x→ 0 (sinx/x)

1

lim x→0 (1-cosx/x)

0

lim x→ +- inf (1 + c/x)^x

e^c

lim x→0+ (1+cx)^1/x

e^c

lim x→ -inf (1/x)

0

lim x→inf (1/x)

0

definition of a derivative (limit of the difference quotient)

f’(x) = f(x+h) - f(x)/h

definition of a derivative (alternate form)

f(x) - f(b)/x-b

normal line

the line perpendicular to to the tangent line at the point of tangency

avg ROC

slope of the secant line

avg roc formula

delta f/ delta x OR delta y/ delta x OR f(b)-f(a)/b-a

not differentiable (3):

1. f not continuous at x = a

2. f has a corner/cusp at x = a

3. f has a vertical tangent at x = a