1. (a) Let {fn}neN : [0,00) + R be a sequence of function define by: sin(nx)...

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1. (a) Let {fn}neN : [0,00) + R be a sequence of function define by: sin(nx) fn(x) 1+ nx (i) Guess the pointwise limit f of f

Answer 1

Answer #1

@ fn (2) sin (na) It na v at [0, do) 0 i fn (0) = 0 In>,1 = lim fn(0) - 0 ! nya for a we have 2 fixed at co do) OL 1 Anca) 1

Let € 70 be Choosen Now xat [a, a) , azo | fn (m) - fca) | = | sirene) ol Itna I sin (na) / It na . El sinna) 1] 1tna < 1 na

111 Let be choosen and nG ło, & Then I fn (2) - fla) 12 ha [prodided in ci) LE if I LE na il if theln it. If notat But I as n

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Answer 2

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