If `lim_(x -> oo) f(x^2) = a` (a finite nubmer), 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?

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)=x+sqrt(x^2+2x) and g(x)=sqrt(x^2+2x-x) , then which of the following is/are true. a. lim_(x->oo)g(x)=1 b. lim_(x->oo)f(x)=1 c. lim_(x->oo)f(x)=-1 d. lim_(x->oo)g(x)=-1

Let f : R to R be a function such that lim_(x to oo) f(x) = M gt 0 . Then which of the following is false?

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

If f:(-oo,3]rarr[7,oo);f(x)=x^(2)-6x+16, then which of the following is true

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

If Lim_(x->oo) (l n(e^2x^2 +5x)-2ln(c^2x+1))=-2 then which of the following may be true -

Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2 - ax + 1)/(x^2+ax+1) ;0 lt a lt 2 . Which of the following is true?

Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2 - ax + 1)/(x^2+ax+1) ;0 lt a lt 2 . Which of the following is true ?