Barrons AP Calculus

(b)

(c)

(b)

By  the Ratio   Test,   the series  converges   when

Thus,   the radius  of  convergence is  e.

(a)  To  find    the     maximum     rate    of  growth,     first   find    the     derivative  of 

,   which   equals  0

when    F   =   300.    A   signs   analysis    shows   that        changes from    positive    to

negative    there,  confirming  that        is  at  its maximum when    there   are 300

trout.

The differential    equation        is  separable.

To  integrate   the left    side    of  this    equation,   use the method  of  partial