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

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Grade 12Differential Calculus

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

Vaibhav Mathur

16 Years agoGrade 12

1 Answer

Ramesh V

16 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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