unit 10

Question 1

parametric formula : dy/dx

Answer 1

dy/dt / dx/dt

Question 2

parametric formula : d^2y/dx^2

Answer 2

d/dt (dy/dt) / dx/dt

Question 3

parametric formula : arc length

Answer 3

∫root((dx/dt)^2+(dy/dt)^2 dt

Question 4

parametric formula: area

Answer 4

+-∫ y(t)x’(t) dt

Question 5

polar formula : dy/dx (slope)

Answer 5

dy/dθ / dx/dθ = rcosθ+r’sinθ / -rsinθ + r-cosθ

Question 6

polar formula: arc length

Answer 6

∫root ((r’cosθ-rsinθ)^2 + (r’sinθ+rcosθ)^2)

Question 7

polar formula: area

Answer 7

1/2∫r^2

Question 8

polar x and y

Answer 8

x=rcos
y=rsin

Question 9

things to know (magnitude) ;

Answer 9

speed= v’t=root ((x’t)^2+(y’t)^2))

Question 9

things to know (acceleration vector)

Answer 9

a(t)=r’‘(t)

Question 9

things to know (derivatives):

Answer 9

1. r’(t)=(x’, y’)= gives velocity vector

Question 9

things to know (displacement and distance traveled)

Answer 9

displacement : r(b) - r(a)
distance: ∫ |v(t)|dt