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Grade: 12

Lim(x tends to infinity)(sin-1x-tan-1 x)2/xn exists  for maximum value of n, is

a. n=2



d.No such value of n is possible

10 years ago

Answers : (1)

Ramesh V
70 Points

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

10 years ago
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