in Calculus
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The interval in which $f(x) = \cot^{-1}x + x$ increases, is

(a) $R$

(b)$(0,\infty )$

(c)$R-[n-\pi]$

(d)None of these
in Calculus
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f'(x) =  -1/(1+x2) + 1

f'(x) will be postive for all the real values cuz of 1/(1+x2) term which always evaluates  to <=1 but >=0

hence,f(x) will be increasing in real domain.

please correct me

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Yeah, your answer is correct, it's given opt(1). :-)
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1 Answer

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Best answer

F(x) is increasing function if F'(x) >=0 (non negative)

here F'(x) =-1/(1+x2) + 1

= x2/(1+x2)

which is always greater than or equal to 0 (means non negative)

becoz both x2 >=0 and (1+x2 ) > 0 

(we know square of the number always non negative )

so here F(x) is increasing for all real number

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