Formulas Flashcards
1
Q
derivative of a^x
A
a^x (ln(a))
2
Q
derivative of loga(x)
A
1/(xlna)
3
Q
derivative of cos(x)
A
-sin(x)
4
Q
derivative of sin(x)
A
cos(x)
5
Q
linear approximation formula
A
f(x) = f’(a)(x-a) + f(a)
6
Q
newtons method
A
x(n+1) = xn - (f(xn) / f’(xn))
7
Q
derivative of arcsin(x)
A
1/ root(1 - x^2)
8
Q
derivative of arccos(x)
A
- 1 / root(1 - x^2)
9
Q
derivative of arctan(x)
A
1 / (1 + x^2)
10
Q
when is there not a global max or min
A
when the function approaches infinity
11
Q
taylor polynomial third degree
A
f(x) = f(a) + f’(a)(x-a) + (f’‘(a)/2!)(x-a)^2 + (f’’‘(a)/3!)(x-a)^3
12
Q
l’hopitals rules
A
lim x>a, f(x)/g(x) is equal to lim x>a, f’(x)/g’(x)
13
Q
trapezoidal rule
A
x = (b-a)/2n
A = x(f(x0) + f(xn) + 2(f(x1) + f(x2)…))
14
Q
area of a circle
A
A = pi(r^2)
15
Q
volume of a cylinder
A
V = pi(r^2)h
