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

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

Grade:12

1 Answers

Ramesh V
70 Points
14 years ago

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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Naga Ramesh
IIT Kgp - 2005 batch

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