The following problems require the use of the algebraic computation of limits of functions as x approaches a constant. Most problems are average. A few are somewhat challenging. All of the solutions are given WITHOUT the use of L'Hopital's Rule. If you are going to try these problems before looking at the solutions, you can avoid common mistakes by giving careful consideration to the form  during the computations of these limits. Initially, many students INCORRECTLY conclude that  is equal to 1 or 0 , or that the limit does not exist or is  or  . In fact, the form  is an example of an indeterminate form. This simply means that you have not yet determined an answer. Usually, this indeterminate form can be circumvented by using algebraic manipulation. Such tools as algebraic simplification, factoring, and conjugates can easily be used to circumvent the form  so that the limit can be calculated.