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If lim(nrarrinfty)(an-frac(1+n^2)(1+n))...

If `lim_(nrarrinfty)(an-frac(1+n^2)(1+n))=b` a finite number then

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))`

Text Solution

Verified by Experts

The correct Answer is:
A, C
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`
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