1. Consider the map xn+1= 2xn/(1+xn). Derive all fixed points and evaluate their stability. Show your work. Answer: 0)1(12=−+=xxxxxsimplifies to… Therefore, x = 0 or 1 are the fixed points. Evaluate the first derivative to determine stability, by the quotient rule the derivative is: ( )1,0211,0)1(*2)1(*2=−=∧∧+−+=xxxxxdxxdf@ ∧x= 0 , ( )2=dxxdf@ ∧x= 1 , ( )5.0=dxxdfTherefore, the fixed point at 0 is unstable and the fixed point at 1 is stable. 2. For each map below, generate cobweb plots to determine the map’s behavior (ignore ranges of inputs that give you imaginary numbers. Use these plots in order to fully describe all fixed points and their stability. a. xn+1 =sqrt(xn) Answer
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