Question: (a) Prove that for any real :2 > 1, we have lim 3:- = ID. 11)00 REMARK: It is true more generally that for any

(a) Prove that for any real :2 > 1, we have

(a) Prove that for any real :2 > 1, we have lim 3:- = ID. 11)00 REMARK: It is true more generally that for any xed I: E ]N, we have lirn H900 other words, exponential growth is faster than polynomial. HINT: Write a = l + b for some $3 > D. (b) Prove that lim \"1/14 = 1. 11100 HINT! Write r11\" = 1 + d?I for some dn ; 0

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