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

*PROBLEM 1 :*Compute .Click HERE to see a detailed solution to problem 1.

*PROBLEM 2 :*Compute .Click HERE to see a detailed solution to problem 2.

*PROBLEM 3 :*Compute .Click HERE to see a detailed solution to problem 3.

*PROBLEM 4 :*Compute .Click HERE to see a detailed solution to problem 4.

*PROBLEM 5 :*Compute .Click HERE to see a detailed solution to problem 5.

*PROBLEM 6 :*Compute .Click HERE to see a detailed solution to problem 6.

*PROBLEM 7 :*Compute .Click HERE to see a detailed solution to problem 7.

*PROBLEM 8 :*Compute .Click HERE to see a detailed solution to problem 8.

*PROBLEM 9 :*Compute .Click HERE to see a detailed solution to problem 9.

*PROBLEM 10 :*Compute .Click HERE to see a detailed solution to problem 10.

*PROBLEM 11 :*Compute .Click HERE to see a detailed solution to problem 11.

*PROBLEM 12 :*Compute .Click HERE to see a detailed solution to problem 12.

*PROBLEM 13 :*Compute .This problem requires an unusual replacement, trigonometry identities, and trigonometry limits.

Click HERE to see a detailed solution to problem 13.

*PROBLEM 14 :*Consider the functioni.) Sketch the graph of

*f*.ii.) Determine the following limits.

- a.)
- b.)
- c.)
- d.)
- e.)
- f.)
- g.)
- h.)
- i.)
- j.)
- k.)
- l.)

Click HERE to see a detailed solution to problem 14.

- a.)
*PROBLEM 15 :*Consider the functionDetermine the values of constants

*a*and*b*so that exists and is equal to f(2).Click HERE to see a detailed solution to problem 15.

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

Mon Aug 26 14:56:41 PDT 1996