Formulas

Question 1

Work

Answer 1

W= ∫F(x) from a to b

Question 2

Speed parametric

Answer 2

√[x’(t)² +y’(t)²]

Question 3

Arc Length parametric

Answer 3

∫√[x’(t)² +y’(t)²] from a to b

Question 4

Amplitude

Answer 4

2π/B

Question 5

Area under a Curve of a Polar Equation

Answer 5

(1/2) ∫f(θ)² from a to b

Question 6

Simpson’s Rule

Answer 6

(Δx/3)( f(x0)+ 4f(x1)+ 2f(x2) . . . . +2(f(x[n-2]))+ 4f(xn-1) + f(xn)

Question 7

Lagrange Error

Answer 7

If P(x) is the nth degree Taylor polynomial of f(x) about c and  for all t between x and c, then f^(n+1) < M for all t  between x and c, then
|f(x)- Pn(x)|<  M/(n+1) |x-c|^(n+1)

Question 8

e^x Maclaurin Series

Answer 8

1+ x + x²/2! +x^3/3! . .Σx^k/k!

Question 9

sin(x) Maclaurin Series

Answer 9

x-x^3/3! + x^5/5! - x^7/7! . . . Σ(-1)^k (x^(2k+1)/(2k+1)!)

Question 10

cos(x) Maclaurin Series

Answer 10

1- x²/2! + x^4/4!- x^6/6! . . . Σ(-1)^k (x^(2k)/(2k)!

Question 11

ln(1+x) Maclaurin Series

Answer 11

x- x²/2 + x^3/3 - x^4/4. . . . Σ(-1)^k (x^(k+1)/(k+1))

Question 12

Derivative of the Inverse of f(x)

Answer 12

1/ f’ (f(inverse of x))

Question 13

Slope of the Polar Equation

Answer 13

[r’(θ)sin(θ) +r(θ)cos(θ)] / [r’(θ)cos(θ) - r(θ)sin (θ)]

Question 14

Sum of a Geometric Series

Answer 14

cr^m/ (1-r)

Question 15

Surface Area- Regular

Answer 15

2π ∫f(x)√ ̅(1+f’(x)²)

Question 16

Surface Area Parametric

Answer 16

2π∫ y(t)√ ̅(y’(t)²+ x’(t)²)

Question 17

Arc Length- Polar

Answer 17

∫√ ̅(f(θ)²+f’(θ)²)

Question 18

Integral of the 1/x^p

Answer 18

If from 0 to a, and p1, a^(1-p)/(p-1)