Homework Help: Calculus (for Business)

Posted by Leah on Saturday, February 6, 2010 at 10:48pm.

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)/(v-u)
Where E is measured in foot-pounds 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

Calculus (for Business) - drwls, Saturday, February 6, 2010 at 11:38pm
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.
Calculus (for Business) - Leah, Monday, February 8, 2010 at 12:30am
Could you please show me the math behind answer a? How did you calculate the limit to get infinity?

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