lim x->8 (1/[p/2-arctan(x)])-(1/arcsin(1/x))

Question

lim x->∞ (1/[π/2-arctan(x)])-(1/arcsin(1/x))

Answer 1

Substitute ∞ into the function.  If the limit is ∞/∞  or  0/0, then the limit is indeterminate.  You have to find derivative of the function until the function is no longer indeterminate.

 

 

I will rewrite the limit function using exponents to ease the differentiation process for you.

 

lim (π/2 - tan^-1(x))^-1 - (sin^-1(x^-1))^-1

x-->∞