(a) State the Mean Value Theorem for integrals. (b) Let P(r, t) is a population density. Then the total population for a

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A State The Mean Value Theorem For Integrals B Let P R T Is A Population Density Then The Total Population For A 1 (46.07 KiB) Viewed 38 times

(a) State the Mean Value Theorem for integrals. (b) Let P(r, t) is a population density. Then the total population for a ≤ x ≤ b is N(t)=P(x, t) dr. Suppose for any a < b that the change in population is dN = F(a) - F(b), dt where F(r) is the flux of individuals moving to the right. Show that Әр OF = 0. Ət Әх 8P (c) Suppose all individuals move to the right with constant velocity c. Show that + c = 0. This is called the first-order wave equation. It is the simplest way to get travelling wave solutions. (Next homework). at (d) Suppose that all individuals instead move such that F(x)=-D. Draw a picture of this and give an interpretation of this movement. (e) Show that if individuals move as in part d), we have the diffusion equation OP = DORP. 8P