e?2?1+2x Limits? Evaluate the following limits. Use l'Hôpital's Rule when needed. lim x2 x?0

Solution Step 1 In this problem we have to evaluate the limit lim e2x1+2x by using l'Hôpital's Rule when x0 x2 needed. l'Hôpital's Rule: f(x) f(x) Suppose that we have one of the following cases, lim = or lim = ± xa g(x) 0 xa 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 gx)