Let `f(x)=lim_(nrarroo) (tan^(-1)(tanx))/(1+(log_(x)x)^(n)),x ne(2n+1)(pi)/(2)` then

Options

A. `AA1ltxlt(pi)/(2),f(x)` is an identity function
B. `AA(pi)/(2)ltxltpi,` the graph of f(x) is a straight line having y intercept of `-pi`
C. `AA(pi)/(2)ltxlte`, the graph of f(x) is a straight line having y intercept of `-pi`
D. `AAxgte, f(x)` is a constant function

Answer

A, C, D

Explanation

`AA1 ltx lt(pi)/(2), tan^(-1)tanx=x`
`and 0 lt log_(e)lt log_(e).(pi)/(2)lt1`
`rArr" "f(x)=x`
`AA(pi)/(2)ltx lte, tan^(-1)tanx=x-pi`
and `0lt log_(e)xlt1`
`therefore" "(log_(e)x)^(n)=0`
`rArr" "f(x)=x-pi`
and for `x gt e, log_(e)xlt1, therefore (log_(e)x)^(n)rarroo`
`rArr" "f(x)=0`