. A sequence x may be defined inductively by specifying a value for the first termand then specifying xn for in terms of earlier values in the sequence.(a) Let and, for Find the first six terms of x anddetermine whether x converges.(b) Let and, for Find the first six terms of xand determine whether x converges.(c) Find the first ten terms of the Fibonnaci sequence f, whereand, for n > 2, fn = fn1 + fn2.(d) If it exists, estimate the limit of the sequence x, where(e) If it exists, estimate the limit of the sequence x, where

9/21/16 ● To show a limit doesn’t exist ○ All #’s can’t exist ■ Prove that left and righthand limits don’t exist or are not equal ■ Or one or both go to infinity ■ One or both onesided limits do not exist Challenge problems 1. Prove lim (x>a) ax^2 + Bx + y = aa^2 + Ba + y 2. Prove that lim (x>0) lim sin (pi/x) does not exist ● Squueze theorem ○ If lim (x>a) f(x) = lim (x>a) g(x) = L and for x near but not equal to a f(x) a) h(x) = L ■ EXAMPLE ● h(x) = x sin x ● What is lim (x>0) h(x) ● 1