Calculus of a Single Variable, Chapter 3, 3.5, Section 3.5, Problem 30

You need to evaluate the limit, hence, you need to replace oo for x in equation:
lim_(x->oo) (5 x^2 + 2)/(sqrt(x^2+3)) = (5 oo + 2)/(sqrt(oo+3)) = (oo)/(oo)
Since the result is indeterminate, you need to factor out x^2 at numerator and x^2 at denominator:
lim_(x->oo)(x^2(5 + 2/x^2))/(sqrt(x^2(1 + 3/x^2)))
lim_(x->oo)(x^2(5 + 2/x^2))/(|x|sqrt(1 + 3/x^2))
Since lim_(x->oo) 2/(x^(3/2)) = 0 and lim_(x->oo) 3/x^2 = 0, yields:
lim_(x->oo) (x^(2-1))*(5/1)= 5*lim_(x->oo) x=5*oo = oo
Hence, evaluating the given limit yields lim_(x->oo) (5 x^2 + 2)/(sqrt(x^2+3)) = oo.