Question: 4 Let en(x) = 1 + 23:1 if, and let e(x) = le en(x). You may assume without proof that this ' 7'1 00 sequence

4 Let en(x) = 1 + 23:1 if, and let e(x) = le en(x). You may assume without proof that this ' 7'1 00 sequence converges for every x 6 R. for all x E [0, 1] and all n E IN. Why does this imply e(x) 1 g Cx for all x E [0, 1]? (b) Prove that 1 C|x[ g e(x) g 1 + C|xl for every x 6 [1,1]. (c) Deduce that e(x) is continuous at O. (a) Find, with justification, a constant C (not depending on x) such that Egzl if

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