Question: Question 1 (a) Find the limits (i) 11m H5534 as>U 3:3 ' (II) lim m (b) Let [3:] denote the greatest integer less than

Question 1 (a) Find the limits (i) 11m " H5534 as>U

Question 1 (a) Find the limits (i) 11m " H5534 as>U 3:3 ' (II) lim m (b) Let [3:] denote the greatest integer less than or equal to 3:. (i) Sketch the function (71)l'\"][a:] for 0 g a: 5 4 and hence evaluate the RiemannStieltjes integral 4 f0 x2d((1)l$] [13]). (ii) Use integration by parts to evaluate the Riemann-Stieltjes integral fuck/5]). (c) For every p E IR, determine whether the integral 00 p 1 2 f a: tan (2: )d3: 0 1 + 1173 is Convergent or not

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