Exam 2 Math

Sinh(x)=

(e^x-e^-x)/2

Cosh(x)=

(e^x+e^-x)/2

d/dx(sinh(x))=

cosh(x)

d/dx(cosh(x))=

sinh(x)

if f’ changes from positive to negative @ c…

local max

of f’ changes fom a negative to a positive @ c

local min

Sin (theta)=

opposite/hypotenuse

Cos(theta)

adjacent/hypotenuse

tan(theta)

opposite/adjacent

csc(theta)=

1/sin(theta)

sec(theta)=

1/cos(theta)

cot(theta)

1/tan(theta)

1+tan²x=

sec²(x)

1+cot²(x)=

csc²(x)

sin(a+/1)=

sinacosb±cosasinb

cos(a+/-b)=

cosacosb±sinasinb

sin(2x)=

2sinxcosx

cos(2x)

cos²x-sin²(x)=2cos²x-1=1-2sin²(x)

lim x→0 sin(x)/x=

1

limx→ 1-cos(x)/x=

0

lim → 1-cos(x)/x²

1/2

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

1/√1-x²

d/dx(cos^-1(x))=

-1/√1-x²

d/dx(tan^-1(x))=

1/(1+x²)

d/dx(cot^-1(x))=

-1/1+x²

d/dx(sec^-1(x))=

1/|x|√x²-1

d/dx(csc^-1(x))=

-1/|x|√x²-1

∫x^ndx=x^(n+1)/(n+1)+C

x^(n+1)/(n+1)+C

∫1/x(dx)=

ln|x|+c

∫e^x(dx)=

e^x+c

∫e^xdx=

e^x+c

∫a^x(dx)=

a^x/ln(a)+c

∫sinx(dx=

-cos(x)+c

∫cosx(dx)=

sin(x)+C

∫√a²-x²(dx)=

x/2√a²-x²+a²/2*arcsin(x/a)+c

∫f(x)=

F(b)-F(a)

the integral of an odd function [-a,a]

=0

Area of a circle

pi r²

circumfrence of a circle

2pir

area of a trapezoid

1/2(b1+b2)h

Perimeter of a trapezoid

a+b+c+d

cylinder area

V=pir²h

surface area of a cylinder

2pir²+2pirh

Volume of a cone

1/3pir²h

surface area of a cone l=sliant hight

pir²+pir(l)

volume of sphere

4/3 pi r ³

surface area of sphere

4phr²