(a) Define in the usual notation, the uniform convergence of a sequence of functions {fn(x)} in the domain J E R. (b) Consider the sequence of functions {fn(x)} defined by, sin(nx + 3) Vn +1 fn(x) = `...

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Extracted text: (a) Define in the usual notation, the uniform convergence of a sequence of functions {fn(x)} in the domain J E R. (b) Consider the sequence of functions {fn(x)} defined by, sin(nx + 3) Vn +1 fn(x) = ` , 2 ER (i) Find the pointwise limit of above sequence of functions. (ii) Prove that {fn} is uniformly convergent on R.