If `lim_(ntooo) (an-(1+n^(2))/(1+n))=b`, where a is a finite number, then

Options

A. `f(0)=1`
B. `f((pi)/(2))=1`
C. `f(a)=(cosa)^(cos^(2)a).(sina)^(sin^(2)a)" if "ain(0,(pi)/(2))`
D. `f(a)=((sina)^(sin^(2)a))/((cosa)^(cos^(2)a))" if "ain(0,(pi)/(2))`

Answer

A, C

Explanation

Limit`=underset(ntooo)lim(an(1+n)-(1+n^(2)))/(1+n)=underset(ntooo)lim((a-1)n^(2)+an-1)/(n+1)`
If `a-1=0," limit "=underset(ntooo)lim(an-1)/(n+1)=a=b`
`:. a=b=1`