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Lim(x tends to infinity)(sin-1x-tan-1 x)2/xn exists for maximum value of n, is
a. n=2
b.n=3
c.n=6
d.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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