calc formulas

a² - b² —> difference of squares

(a-b)(a+b)

a³ + b³

(a+b)(a²-ab+b²)

a³ - b³

(a-b)(a²+ab+b²)

(a ± b)² —> perfect square

a² ± 2ab + b²

(a+b)³

a³ + 3a²b +3ab² + b³

(a-b)³

a³ + 3a²b - 3ab² - b³

quadratic formula

-b ± sqrt(b² - 4ac) / 2a

AROC formula

y₂ - y₁ / x₂ - x₁

IROC formula

f(x+h) - f(x) / h

cube surface area and volume formulas

SA: 6a²

V: a³

rectangular prism surface area and volume formulas

SA: 2(lw+lh+wh)

V: l*w*h

sphere surface area and volume formulas

SA: 4(pi)r²

V: 4/3(pi)r³

cylindrical prism surface area and volume formulas

SA: 2(pi)r*h+2(pi)r²
V: pi(r²)h

vertical asymptote

lim_x→a = n/0, asymptote at x => ± infinity

hole

x→a^- = x →a⁺ but at a = 0/0

horizontal asymptote

if lim x→ ± infinity where f(x)= constant

f(x) = p(x)/q(x)
- degree of denominator higher than numerator, HA at y=0

- degree of numerator higher than denominator, no HA

- degree of numerator = denominator, HA at numerator degree / denominator degree

definition of a derivitive

IROC formula → f’(x)=lim f(x+h)-f(x)/h

constant rule

c’ = 0

power rule

xⁿ’ = nx^n-1

constant multiple rule

cf(x)’ = cf’(x)

sum and difference rule

[f(x)±g(x)]’ = f’(x)±g(x)’

tangent line

y-f(a) = f’(a)(x-a)

• x,y = given point

• f(a)= y at a

• f’(a) = slope at a

product rule

[f(x)g(x)] = f’(x)g(x)+f(x)g’(x)

quotient rule

[f(x)/g(x)]’ = f’(x)g(x)-f(x)g’(x)/g(x)²

chain rule

f(g(x)) = f’(g(x))g’(x)

derivative of f(x) while g(x) stays the same, multiplied by derivative of g(x)