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If the domain of the function f(x)=sin^(...

If the domain of the function f(x)=`sin^(-1)(log_(2)((x)/(2)))` is [a,b], then the value of `lim_(x rarr0)(1+ln(a+bx))^(1/x)`= is equal to
`(A) e (B) e^(2) (C) e^(3) (D) e^(4)`

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