Assignment #13

In order to find the volume (V) of the solid when revolving "f(x)=1/x" about the x-axis you must do the following:

V=integral of (1/x)dx * pi [0,infinite)

V=(ln infinite - ln(1)) * pi 

V=pi

In order to find the Surface Area (SA) you must do the following:

SA=((1-(x^(-4)))^(1/2))dx from [1,infinite) * pi * integral of 1/(x^2)dx

SA=infinite

This is not a paradox because the volume approaches a finite number (pi) as the function approaches infinite and the surface area does not approach a finite number as the function approaches infinite.

Assignment #12

This What If talks about Fairy Demographics. It relates to the logistic curve as it talks about both the human and fairy populations and how they increase/decrease in the environment. Fairy demographics differ a bit as fairies are immortal meaning they do not simply vanish (unless something learns to kill them off). The fairy population keeps growing as the human population keeps growing because both correlate. As humans reach the environmental carrying capacity of 9 billion however, it will be difficult for them to survive and the human population will decrease. The fairy population, on the other hand, would level off (it will not increase or decrease) as fairies are immortal.