Calculus (for Business)
posted by Leah .
Suppose a fish swimming a distance of L ft at a speed of v fit/sec relative to the water against a current flowing at the rate of u ft/sec (u<v) expends a total energy given by
E(v)= (aLv^3)/(vu)
Where E is measured in footpounds and a is a constant.
a) Evaluate the limit of E(v) as v>u+ and interpret your result
b) Evaluate the limit of E(v) as v>infinity and interpret your result

a) as v > u the Energy required becomes infinite because the fish does not move and requires infinite time to go a distance L.
b) as v> infinity, the energy required is proportional to v^2 (which is true for the fluid drag force), as the stream velocity becomes negligible compared to v.
Energy = force x distance. 
Could you please show me the math behind answer a? How did you calculate the limit to get infinity?