Calculus 1: Formulas

a² - b² =

(a-b)(a+b)

(a+b)² =

a² + 2ab + b²

(a-b)² =

a² - 2ab + b²

a³ - b³ =

(a-b)(a² + ab + b²)

a³ + b³ =

(a+b)(a² - ab + b²)

x → c -

left hand

x → c +

right hand

x → c

overall limit

lim (number) =

x → c (value)

number

lim (x) =

x → c (value)

c (value)

lim ( f(x) ± g(x) ) =

x → c

f(x) ± g(x)

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

x → c

f(x) g(x)

lim f(x)/ g(x) =

x → c

f(x) / g(x), but g(x) ≠ 0

lim (number * f(x) ) =

x → c

number * f(x)

lim number ^f(x) =

x → c

number ^ raised limit ( llim f(x) x → c)

sec (x) =

1/cos(x)

csc (x) =

1/sin(x)

tan (x) =

sin(x)/cos(x)

cot (x) =

cos(x)/sin(x)

sin²(x) + cos²(x) =

1

1 + tan²(x) =

sec²(x)

1 + cot² (x) =

csc²(x)

y=f(x) + c

shifts the graph c units up

y=f(x) - c

shifts the graph c units down

y=f(x+c)

shifts the graph c units to the left

y=f(x-c)

shifts the graph c units to the right =y

y=-f(x)

reflects about x-axis

y=f(-x)

reflects about y-axis