Chapter 6.1, Problem 31P

1. A Blue Whale's resting heart rate has period that happens to be approximately equal to 2π. A typical ECG of a whale's heartbeat over one period may be approximated by the function, f(x) = 0.005x4 2 0.005x³-0.364x² + 1.27x on the interval [0, 27]. Find an nth-order Fourier approximation to the Blue Whale's heartbeat, where n ≥ 3 is different from that used in any other posts on this topic, to generate a periodic function that can be used to model its heartbeat, and graph your result. Be sure to include your chosen value of n in your Subject Heading.

7. The demand for a product, in dollars, is p = D(x) = 1000 -0.5 -0.0002x² 1 Find the consumer surplus when the sales level is 200. [Hints: Let pm be the market price when xm units of product are sold. Then the consumer surplus can be calculated by foam (D(x) — pm) dx]

4. Find the general solution and the definite solution for the following differential equations: (a) +10y=15, y(0) = 0; (b) 2 + 4y = 6, y(0) =