Assignment #13

In order to find the volume of the solid when revolving f(x)=1/x around the x-axis you must do V=integral of (1/x)dx*π  [0,∞) V=(ln∞-ln(1))*π V=π

In order to find the surface area you do
Surface Area=((1-(x^-4)^1/2))dx from [1,∞)*π*ʃ1/(x^2)dx = ∞

This isn't a paradox because the volume of the solid approaches π as the functions continues unto ∞ and while the surface area does not approach a definite integer while the function continues to approach ∞.

Assignment #12

This what if is about the demographics of Fairies. It relates to the logistic curve with both human and fairy populations and how they increase or decrease in the environment. As the human population increases so does the fairy population. The fairies are also immortal, meaning they cannot die unless something learns how to kill them. As the human population increases the carrying capacity, eventually the population would decrease slightly and since there is a direct relation to the fairy population, but they are immortal, the fairy population levels off and stays at a specific population.