Question #82487
Qno. 3) I) let X1=8 and Xn+1=1/2Xn+2 for all n belongs to N .show that X is bounded and monotone.also find the limit.
ii) let X1>1 and Xn+1=2-1/Xn for all n belongs to N. Show that (Xn) is bounded and monotone . Find the limits.
ii) let X1>1 and Xn+1=2-1/Xn for all n belongs to N. Show that (Xn) is bounded and monotone . Find the limits.
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Let φ(x) = 1 4 + x − x 2 . For a given r ∈ R, consider the sequence {xn}, which is defined by x1 = r and xn+1 = φ(xn), n ∈ N. If the sequence converges, let r∞ be the limit. (a) For r = 0, prove that {xn} is bounded and monotonic. Find r∞ = β. (b) Find all r 6= 0 such that r∞ = β. (