Abelian_Math
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1.
Let c be a positive number, and let A > 0 represent the initial value of a population.
a) Show that the function p(t) = (A^(-c) - ct)^(-1/c) satisfies the differential equation
p'(t) = (p(t))^(1+c)
b) What happens to p(t) as t > (A^(-c)/c) from the left?
2. Find the Maclaurin series for the functions sinh(x) and cosh(x) by using the Maclaurin
series for ex and the defnitions of sinh(x) and cosh(x) in terms of ex. Compute the radius
of convergence for each series.
Let c be a positive number, and let A > 0 represent the initial value of a population.
a) Show that the function p(t) = (A^(-c) - ct)^(-1/c) satisfies the differential equation
p'(t) = (p(t))^(1+c)
b) What happens to p(t) as t > (A^(-c)/c) from the left?
2. Find the Maclaurin series for the functions sinh(x) and cosh(x) by using the Maclaurin
series for ex and the defnitions of sinh(x) and cosh(x) in terms of ex. Compute the radius
of convergence for each series.