1.

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

Answer»

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

Solution :`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`


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