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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
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 -- Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Naga Ramesh IIT Kgp - 2005 batch
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
--
Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Naga Ramesh IIT Kgp - 2005 batch
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