Let `f(x) =x+sqrt(x^2+2x)` and `g(x) =sqrt(x^2+2x)-x` then (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(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(x)=lim_(n->oo)(2x^(2n)sin(1/x)+x)/(1+x^(2n)) then find (a) lim_(x->oo) xf(x) (b) lim_(x->1) f(x) (c) lim_(x->0) f(x) (d) lim_(x->-oo) f(x)

lim_(x->oo) (x-sqrt(x^2-1))

Let f(x)=lim_(n rarr oo)(2x^(2n)sin\ 1/x+x)/(1+x^(2n)) then find (a) lim_(x rarr oo) x f(x) (b) lim_(x rarr 1) f(x)

If f(x) = sqrt((x-sinx)/(x+cos^(2)x)) , then lim_(x rarr oo) f(x) =

Given f(x)=(ax+b)/(x+1), lim_(x to oo)f(x)=1 and lim_(x to 0)f(x)=2 , then f(-2) is

lim_(x rarr oo) (1+f(x))^(1/f(x))

Let f(x)=(lim)_(n->oo)(2x^(2n)sin1/x+x)/(1+x^(2n))\ then find :\ (lim)_(x->-oo)f(x)

If (5x-2)/x lt f(x) lt (5x^2-4x)/x^2 and (sinx^2)/x lt g (x) lt (log (1+x^2))/x then |lim_( xtooo)f(x) -lim_( x to oo) g(x)| is equal to

lim_(x rarr oo)(sqrt(x^(2)+x+1)-sqrt(x^2+1))