A bit unorthodox, but that works. you forgot one thing though:
The question is to find the limit as x->inf of x/sqr(1+(x/c)^2) where c is a constant. I rewrote the equation as sqr(x^2*c^2/(x^2+c^2)). Then find the limit of what is inside the square root ie. x^2*c^2/(x^2+c^2). This comes to c^2 the square root of which is c.
Is this the correct and most appropriate way of arriving at the limit?