Math 132: Calculus for Physical and Life Sciences 2 Problem Set 7 Due Friday, April 4, 2008, at the beginning of class. Selected answers

1. (b) (c)

(Note that the default grid of points used by Maple to generate its plot of the direction field uses more finely spaced points than the integer grid specified in the problem, so this shows more detail. In the solution you hand in, follow the given directions – do not try to reproduce this picture!)

(d) y(1) ≈ 2.97664

3. (a) y = arcsin (A\sqrt{|\frac{x + 1}{x + 3}|})

(c) y = 4e^{x^{2}}

(e) y = −\frac{1}{x^{2} + x^{3} − 1}

5. (a) T (25) ≈ 13.2^{∘}

6. (a) \frac{dP}{dt} = −k\sqrt{P}

(c) The population will disappear entirely after 20 weeks.