Math Review

lim x→0, sin x/x =1

1

lim x→0, x/sin x

1

lim x→0 cot ax/cot bx

b/a

lim x→0 csc ax/csc bx

b/a

lim x→0 sin ax/sin bx

a/b

lim x→0 sin ax/ bx

a/b

lim x→0 tan ax/bx

a/b

lim x→0 tan ax/tan bx

a/b

lim x→0 x/cos(x)-1

DNE

lim x→0 x/1 - cos(x)

DNE

lim x→0 1 - cos(x)/x

0

lim x→0 cos(x)-1/x

0

lim x→0 sin ax/tan bx

a/b

lim x→0 tanx/x

1

lim x→0 bx/tanax

b/a

lim x→0 bx/sin ax

b/a

a³+b³

(a+b)(a²-ab+b²)

a³-b³

(a-b)(a²+ab+b²)

sin(2x)=

2sin(x)cos(x)

cos(2x)=

cos²(x)-sin²(x)=1-2sin²(x)=2cos²(x)-1

sin²(x)+cos²(x)=

1

tan²(x)+1=

sec²(x)

1+cot²(x)=

csc²(x)

derivative of a^u

ln(a) times a^u times u’

log(base a)(u)

u’/(ln(a))(u)