Unit 2 Test

Question 1

Arc Length

Answer 1

int(sqrt(1+f’(x)^2)))

Question 2

Surface Area

Answer 2

SA= int f(x)(sqrt(1+f’(x))

Question 3

Taylor Polynomial

Answer 3

f(a) + f’(a)/1!(x-a) +f’‘(a)/2!(x-a)^2

Question 4

Newton Law of Cooling

Answer 4

y'= -k(y-T0)
y= T0 +Ce^-kt

Question 5

Free Fall with resistance

Answer 5

v'= -k/m (v+ mg/k)
v= -mg/k + Ce^-(k/m)t
m= mass
k= air resistance
g= acceleration

Question 6

Continuous Annuity

Answer 6

P’= r(P-N/r)
P= N/r + Ce^(rt)
r= interest rate
n=withdrawal rate

Question 7

First Order Linear Equation

Answer 7

y’ + A(x)y= B(x)
a(x)= e^(intA(x))
y= 1/a(x)(int a(x)B(x)dx+C)

Question 8

Logistic Equation

Answer 8

dy/dt= ky(1-y/A)
y0/(y0-A)= C
y= A/ 1-e^(-kt)/C

Question 9

Logistic Limits

Answer 9

y0>A y(t) is decreasing approaches A as t -> infinity
0 infinity
y0<0 y(t) is decreasing lim approaches negative inf as t approaches infinity

Question 10

Terminal Velocity

Answer 10

mg/k= Vt