`lim_(xto oo) (int_(0)^(x)tan^(-1)dt)/(sqrt(x^(2)+1))` is equal to
`lim_(xto oo) (int_(0)^(x)tan^(-1)dt)/(sqrt(x^(2)+1))` is equal to
A. `(pi)/2`
B. `(pi)/4`
C. 1
D. `pi`
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Correct Answer - A
`lim_(xto oo) (int_(0)^(x)tan^(-1)tdt)/(sqrt(x^(2)+1))` (`(oo)/(oo)` form)
`=lim_(xto oo) (tan^(-1))/(x/(sqrt(x^(2)+1)))`
`=(pi)/2 lim_(xto oo) (sqrt(x^(2)+1))/x`
`=(pi)/2 lim_(xto oo) sqrt(1+1/(x^(2)))=(pi)/2`
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