If `alpha` is the root of the equation `x-tanx=3` where `alpha epsilon((pi)/2,(3pi)/2)`, then which of the following is/are correct? (where [.] denotes the greatest integer function and {.} fractional part function)

Options

A. `lim_(xtoalpha^(+))[("max"(tanx, {x}))/(x-3)]=1`
B. `lim_(xtoalpha^(+))[("mi"(tanx, {x}))/(x-3)]=1`
C. `lim_(xtoalpha^(-))[("min"(tanx, {x}))/(x-3)]=0`
D. `lim_(xtoalpha^(-))[("max"(tanx,{x}))/(tannx)]=1`

Answer

A, B, C, D

Explanation

Shown in the figure