For each of the following statements decide whether it is true or false. If it i
ID: 2882448 • Letter: F
Question
For each of the following statements decide whether it is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. (a) There is one equation x' = f(x) such that every integer is an equilibrium, and there are no other equilibrium points. (b) There is an equation x' = f(x) such that it has exactly three distinct equilibria, and all of them are stable. (c) Suppose f: [a, b) times R rightarrow R is continuous and consider the differential equation y' = f(t, y). There exists at least one solution defined on the interval [a, b]. (d) Let (X, rho) be a complete metric space and suppose g X rightarrow X. If rho(g(x), g (y))Explanation / Answer
(a) True
(b) False . The equations descibes the slope and it has infinite points of eqillibrium.
(c) True
(d) False . For this the comparitive sign should have been greater than sign. As x, y are in the same space as that of X i.e g .
(e) True
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