MATH100 FINAL MEMORIZE

area of circle

πr²

area of sphere

4πr²

volume of sphere

4/3 πr³

area of cylinder

2πr² + 2πrh

volume of cylinder

πr²h

arcsinx

arccosx

arctanx

special triangles

logx taylors

cosx taylors

sinx taylors

e^x taylors

1/(1-x)

taylors polynomial

P(x) = f(a) + f’(a)(x-a) + (f’’(a)(x-a)²)/2! …

newtons method

x_n+1 = x_n - f(x_n)/f’(x_n)

eulers method

x_n = x_n-1 + h

y_n = y_n-1 + hf(x_n-1, y_n-1)

initial condition is your starting point (x_n, y_n)

h = stepsize

approximating y(x_f) x_f = final x_n

linear approx multivariable

f(x,y) = f(a,b) + df/dx(a,b)(x-a)+df/dy(a,b)(y-b)

critical points multivariable

D(x) = fxx*fyy - (fxy)²

D(x) > 0 fxx > 0 → local min

D(x) > 0 fxx < 0 → local max

D(x) = 0 → saddle point

(f○g)(x)

plugging in g(x) as x in f(x)

quadratic formula

b±√(b²-4ac))/(2a)