? 0 0 1 ,0 ,? forms ?Evaluate the following limits. Check your results by graphing. lim(1? ) 3 x x?? x

Solution Step 1 3 x In this problem we have to evaluate lim (1 ) x x By direct substitution of limit, we get 3 x x(1 )x= 1 Thus lim (1 ) has the indeterminate form 1 . x x To evaluate this limit we will be using the following two steps: Assume limf(x) g(x)has the indeterminate form 0 1 , . 0 xa 0 1. Evaluate L = limg(x)ln f(x).This limit can often be put in the form 0or both of which xa can be handled by l’hopital’s rule. g(x) L 2. Then limf(x) = e xa l'Hôpital's Rule: f(x) 0 f(x) ± Suppose that we have one of the following cases, lim xa g(x)= 0or lxa g(x)= ± Where a can be any real number, infinity or negative infinity. In these cases we have lim f(x)= lim f(x) xa g(x) xa g(x)