If `phi(x)=lim_(x->oo)(x^(2n)(f(x)+g(x)))/(1+x^(2n))` then which of the following is correct

If phi(x)=lim_(n->oo)(x^(2n)(f(x)+g(x)))/(1+x^(2n)) then which of the following is correct

If phi(x)=lim_(nrarrinfty)(x^(2n)f(x)+g(x))/(1+x^(2n)) , then

Let f(x)=lim_(nto oo) (2x^(2n) sin (1)/(x)+x)/(1+x^(2n)) , then which of the following alternative(s) is/ are correct?

Let f(x)=lim_(n->oo)(log(2+x)-x^(2n)sinx)/(1+x^(2n)) . then

If f (x) = lim _( n to oo) (n (x ^(1//n)-1)) for x gt 0, then which of the following is/are true?

If f (x) = lim _( n to oo) (n (x ^(1//n)-1)) for x gt 0, then which of the following is/are true?

Let f(x)=lim_(n rarr oo)(log(2+x)-x^(2n)sin x)/(1+x^(2n)) then

The function defined as f(x)=lim_(n rarr oo){cos^(2n)x if x which of the following is correct

If f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1) then range of f(x) is