Calculus

Area of a circle

A=πr²

Area of a trapezoid

A=(b₁-b₂)/2

Volume of a pyramid

V=(1/3)bh

Area of a triangle

A=(1/2)bh

Lateral surface area of a cylinder

S=2πrh

Circumference of a circle

C=2πr or C=πd

Surface area of a sphere

S=4πr²

Total surface area of a cylinder

S=2πrh+2πr²

Volume of a cone

V=(1/3)πr²h

Volume of a cylinder

V=πr²h

volume of a sphere

V=(4/3)πr³

Double angle identity for cos²x

(1+cos2x)/2

Double angle identity for sin²x

(1-cos2x)/2

sin2x

2sinxcosx

cos²x + sin²x

1

1 + cot²x

csc²x

1 + tan²x

sec²x

1/sinx

cscx

1/tanx

cotx

1/cosx

secx

cosx/sinx

cotx

sinx/cosx

tanx

log_ab=c

a^c=b

log(AB)

logA + logB

log(A/B)

LogA-LogB

logA^x

xlogA

lne

1

ln1

0

cos2x

cos²x-sin²x or 2cos²x-1 or 1-2sin²x

e^lnx

x

Odd Function (function symmetrical through the origin)

f(-x) = -f(x)

Even Function (function symmetrical across y-axis)

f(-x) = f(x)

lim(k*f(x))

k*lim(f(x))

lim/x_a f(x)=±infinity

the graph of f has a vertical asymptote at x=a

lim(f(x) ± g(x))

limf(x) ± limg(x)

lim(f(x) * g(x))

limf(x) * limg(x)

limx_0(sinx/x)

1

lim x_0 (cosx-1)/x

0

lim x_infinity (1+1/x)^x

e