If $$y=2x-$$$$tan$$$$-1x-logx+1+x2$$, then:

Correct option is 4y increases in (-∞,∞)

Questions

$If y = 2 x - \tan^{- 1} x - \log \{x + \sqrt{(1 + x^{2})}\}, then:$

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y increases in [0,∞)

y decreases in [0,∞)

y increases in (-∞,0)

y increases in (-∞,∞)

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detailed solution

Correct option is D

y=2x−tan−1x−logx+1+x2⇒dydx=2−11+x2−1+2x21+x2x+1+x2 =2−11+x2−11+x2 =2+2x2−1−1+x21+x2 =1+2x2−1+x21+x2≥0∀x∈R Hence y increases in (-∞,∞)

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If y=2x-tan-1x-logx+1+x2, then:

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$If y = 2 x - \tan^{- 1} x - \log \{x + \sqrt{(1 + x^{2})}\}, then:$