Two methods? Evaluate the following limits in two different ways: Use the methods 4 of Chapter 2and use l'Hôpital's Rule. lim 4x ??x x?? 2x + x?1

Solution Step 1 4x x In this problem we have to find the value of lim 2x + x1in two different ways. 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: Suppose that we have one of the following cases, lim f(x)= or lim f(x= ± xa g(x) 0 xa g(x) ± Where a can be any real number, infinity or negative infinity. f(x) f(x) In these cases we have lim g(x)= lim gx) xa xa