AP Calc (equations to memorize)

1

2sinθcosθ

cos²(θ) - sin²(θ)

2cos²θ-1

1-sin²θ

log_b x + log_b y

log_b x - log_b y

nlog_b x

L±K

L*K

L/K

L^n

a*K

a* limx→c g(x)

1

0

lim h→0 (f(x+h)-f(x)) /h

P(x) = x^n

P’(x) = nx^n-1

First d-last + Last d-first

low* d-high - hi* d-low/ (low)²

cos(x)

-sin(x)

sec²x

sec(x)tan(x)

-csc²(x)

-csc(x)cot(x)

f’(g(x)) * g’(x)

f’(u) * u’

e^f(x) * f’(x)

1/ (√1-x²)

-1/(√1-x²)

1/(1+x²)

a^u * ln(a)* u

1/x

a^x * ln(x)

1/ (xlnb)

(1/(u*lnb))*u’

∫f(x) + ∫g(x)

c*∫f(x)dx

∫x^n dx

((x^n+1)/n-1) + c

0

-a∫b f(x) dx

a∫c f(x)dx + c∫b f(x)dx

c* a∫b f(x)dx

a∫b f(x)dx + a∫b g(x)dx

f(C)= 1/(b-a) a∫b f(x)dx

lxl

a∫b f(x)dx = F(x)lab

F(b)-F(a)

lnlul+c

e^u +c

a^u /lna +c

sin^-1 x +c

tan^-1 x +c

1/√(1-u²) * u’

1/(1+u²) * u’

sin^-1 (u/a) + c

1/a tan^-1 (u/a) +c

(1/2)((b-a)/N)(f(x)+…fN(x))

sec² (x)

-csc² (x)

sec(x)tan(x)

-csc(x)cot(x)

-ln l cos(u)+c l

ln lsin(u)l + c

ln lsec(u) + tan(u)l + c

-ln lcdc(u) + cot(u)l + c

tan u + c

-cot u + c

sec u + c

-csc u + c

s²

((√3)/4) s²

base * height

π/8 (s)²

f’(C) = lim x→ c (f(x)-f(C))/x-c

f(b) - f(a) / b-a

If the function f(x) is continuous on [a,b], and y is a number between f(a) and f(b), then there exists at least one number x=c in the open interval (a,b) such that f(C)=y