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B
(1,∞)
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C
(−∞,−1)
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D
(−∞,∞)
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Solution
The correct options are B(1,∞) D(−∞,−1) y=x/(1+x2) y′=(1+x2)−2x⋅x(1+x2)2=1−x2(1+x2)2 Since (1+x2)2>0 for all x Therefore y′<0 for 1−x2<0 ⇒x>1 or x<−1 Therefore, x∈(−∞,−1) or x∈(1,∞). Thus x/(1+x2) decreases in (−∞,−1] or [1,∞). Ans: B,C