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115_pdfsam_math 54 differential equation solutions odd

# 115_pdfsam_math 54 differential equation solutions odd -...

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Exercises 3.2 16. By definition, p ( t ) = lim h 0 p ( t + h ) p ( t ) h . Replacing h by h in the above equation, we obtain p ( t ) = lim h 0 p ( t h ) p ( t ) h = lim h 0 p ( t ) p ( t h ) h . Adding the previous two equations together yields 2 p ( t ) = lim h 0 p ( t + h ) p ( t ) h + p ( t ) p ( t h ) h = lim h 0 p ( t + h ) p ( t h ) h . Thus p ( t ) = lim h 0 p ( t + h ) p ( t h ) 2 h . 19. This problem can be regarded as a compartmental analysis problem for the population of fish. If we let m ( t ) denote the mass in million tons of a certain species of fish, then the mathematical model for this process is given by dm dt = increase rate decrease rate . The increase rate of fish is given by 2 m million tons/yr. The decrease rate of fish is given as
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