IIT JAM Follow
December 1, 2020 2:47 pm 30 pts
16. Which of the following is true Very uniformly convergent sequence is pointwise conveiecn (B) Eve pointwise convergent sequence is uniformly convergent. (C)Every sequence has a convergent subsequence. (D) None of these and g are bounded and integrable functions on [a, b] then Fj-8i integrable over [a, b] and (A) Fde=-f dr+gds (8)Fd rd-d (C)Fdr-rd- gd (D) None of these 18. Let {f,} be a sequence of functions such that lim S,x) = f(x), x e [a, b] no, and let M,=sup 1S,x)-fa)|. xe[a, b] Then S f uniformly on [a, b] if and only if: (A) M, 0 asnco (B) M, 1 as n0o (C) M,-1 as n 0o (D) None of these