Two methods? Evaluate the following limits in two different ways: Use the methods 5 of Chapter 2 and use l'Hôpital's Rule. lim 2x ? x +1 x?? 5x + x

Solution Step 1 5 In this problem we have to find the value of lim 2x 6 x +1in two different ways. x 5x + x The first method is to simplify the given problem and then apply the limit and the second method is to use l’hopital’s rule. l'Hôpital's Rule: f(x) 0 f(x) ± Suppose that we have one of the following cases, lim g(x) = 0 or lim g(x) = ± xa xa Where a can be any real number, infinity or negative infinity. f(x) f(x) In these cases we have lim = lim xa g(x) xa g(x)