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 tex2html_wrap_inline107 during the computations of these limits. Initially, many students INCORRECTLY conclude that tex2html_wrap_inline107 is equal to 1 or 0 , or that the limit does not exist or is tex2html_wrap_inline115 or tex2html_wrap_inline117 . In fact, the form tex2html_wrap_inline107 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 tex2html_wrap_inline107 so that the limit can be calculated.

The next problem requires an understanding of one-sided limits.

Click HERE to return to the original list of various types of calculus problems.

Your comments and suggestions are welcome. Please e-mail any correspondence to Duane Kouba by clicking on the following address :

Duane Kouba
Mon Aug 26 14:56:41 PDT 1996