Question: For any positive integer n, let S, (0, 0) R be defined by S, (x) =cot (1+(k+1)x2) k=1 where for any x = R,

For any positive integer n, let S, (0, 0) R be defined by S, (x) =cot (1+(k+1)x2) k=1 where for any x = R, cot '(x) = (0, ) and tan-1(x) E 2'2 Then which of the following statemen is(are) TRUE? TU 1+11x2 (A) S (x) = tan-1 for all x>0 , 2 10x (C) The equation S3 (x) = 4 has a root in (0, ) (B) lim cot (S, (x)) = x, for all x>0 n- (D) tan(S, (x)) 1, for all n 1 and x > 0

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