Lim(x tends to infinity)(sin-1x-tan-1 x)2/xn exists for maximum value of n, isa. n=2b.n=3c.n=6d.No such value of n is possible

For any values of x , sin^-1x  lies in ( -Pi/2, Pi/2 )

also ,  -Pi/2 <  tan^-1x  < Pi/2

and here as x tends to infinity , tan^-1x = Pi/2

therefore, as x tends to infinity , (sin^-1x - tan^-1x)² becomes some positive number( >=0 )

also xⁿ goes to +infinity for any value of n(n>0)

so, the final limit to zero ( i.e., limit exists ) for all n>0

from the options max alue of n is 6

so,option C

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