Given the logistic map Xn+1 = run(1 – Xn) with r > 0. Show the 2-cycle is stable for 3 <r <1+V6.
please include the graph 1. Expand 7T if 0 <<< f(x) = 1 if <<, in a half-range: (a) Sine series. (b) Cosine series.
If tan = TT TT << 2 2 then sin =
6. Find the particular part of the solution of the difference equation y(n+2) – 2y(n+1)+y(n) = 4 for n <0.
Exercise 1.20. Show that the series 7t 12 +22m-52 32z-10m2 converges absolutely for |2l< 1
sin (x - 1) x-TT x <T Given f(x) = x2 · Tex + 1, x > Determine if the graph is continuous at it (Show all work)
Please Prove. Prove 2 n > n2 by induction using a basis > 4: Basis: n 5 32> 25 Assume: Prove:
Theory 00 2. Prove that if Vlan] < 1 then an converges. n=1
Q2: Find the complex Fourier series (show your steps) - T < x <07 f(x) 0 < x < Q1: Find the Fourier transform for (show your steps) - 1<x< 0 Otherwise (хе f(x) = { 0,
1) Give a combinatorial proof of the following identity (0 <k<n): n2 k ---- = n.29-1 ke=0