Formulas

Question 1

derivative of a^x

Answer 1

a^x (ln(a))

Question 2

derivative of loga(x)

Answer 2

1/(xlna)

Question 3

derivative of cos(x)

Answer 3

-sin(x)

Question 4

derivative of sin(x)

Answer 4

cos(x)

Question 5

linear approximation formula

Answer 5

f(x) = f’(a)(x-a) + f(a)

Question 6

newtons method

Answer 6

x(n+1) = xn - (f(xn) / f’(xn))

Question 7

derivative of arcsin(x)

Answer 7

1/ root(1 - x^2)

Question 8

derivative of arccos(x)

Answer 8

• 1 / root(1 - x^2)

Question 9

derivative of arctan(x)

Answer 9

1 / (1 + x^2)

Question 10

when is there not a global max or min

Answer 10

when the function approaches infinity

Question 11

taylor polynomial third degree

Answer 11

f(x) = f(a) + f’(a)(x-a) + (f’‘(a)/2!)(x-a)^2 + (f’’‘(a)/3!)(x-a)^3

Question 12

l’hopitals rules

Answer 12

lim x>a, f(x)/g(x) is equal to lim x>a, f’(x)/g’(x)

Question 13

trapezoidal rule

Answer 13

x = (b-a)/2n
A = x(f(x0) + f(xn) + 2(f(x1) + f(x2)…))

Question 14

area of a circle

Answer 14

A = pi(r^2)

Question 15

volume of a cylinder

Answer 15

V = pi(r^2)h

Question 16

trig identity

Answer 16

sin^2(x) + cos^2(x) = 1

Question 17

integration by parts formula

Answer 17

integral udv = uv - intergal vdu

Question 18

average value

Answer 18

1/(b-a) intergral b,a

Question 19

quadratic formula

Answer 19

(-b +/- root(b^2 - 4ac))/2a