Units 7 and 8 Flashcards
1
Q
Euler’s method
A
y1= y0 + y’/\X
2
Q
Differentials
A
dy/dx = ky(a-y)
(y=a is carrying capacity)
dP/dt =kP(1- P/L)
- p= population
- L = carrying capacity
3
Q
Average value of a function
A
1/(b-a) S (f(x) dx)
4
Q
Arc length
A
S (sqrt(1-(y’)^2)) dx
5
Q
Area between curves
A
S f(x)-g(x) dx
- f(x) is top
6
Q
Volume by cross section square
A
- square: S f(x)^2 dx
7
Q
Solids of rotation washer
A
pi * S (x-f(x))^2 - (x-g(x))^2 dx
8
Q
Solids of rotation disk
A
pi * S (x-f(x))^2 dx
9
Q
velocity using a’
A
V(t)=d/dt * a(t)
10
Q
Volume by cross section RIGHT isoceles triangle
A
- isoceles: 0.5 * S f(x)^2 dx
11
Q
Volume by cross section isoceles triangle
A
- isoceles right: sqrt3/4 * S f(x)^2 dx
12
Q
Volume by cross section semicircle
A
- semicircle: pi/8 * S f(x)^2 dx
