For 3(b) Let the function f: R→ R be defined by1x2f(x) =0,x=0,x = 0. Question 3For each nEN, consider xn(a)(b)nX(ii)with x ER+. Define the sequence {gn} by8n(x) = f(xn) =Find the limit function of {gn}, if exists.==121XnXER+.Choose ONE method below to explain whether {gn} converges uniformly onA = [1,2) CR+.(i)By using limit criterion.ORBy using Cauchy criterion for uniform convergence. (Include all analysis.)

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Question 3 For each nEN, consider xn (a) (b) n == X with x ER+. Define the sequence {gn} by 8n(x) = f(xn) = Find the limit function of {gn}, if exists. (ii) —— 1 21 Xn XER+. Choose ONE method below to explain whether {gn} converges uniformly on A = [1,2) CR+. (i) By using limit criterion. OR By using Cauchy criterion for uniform convergence. (Include all analysis.)