The following problems require the algebraic computation of limits of functions as x approaches plus or minus infinity. 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 forms and during the computations of these limits. Initially, many students INCORRECTLY conclude that is equal to 1 , or that the limit does not exist, or is or . Many also conclude that is equal to 0 . In fact, the forms and are examples of

*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 .Click HERE to see a detailed solution to problem 13.

*PROBLEM 14 :*Compute .Click HERE to see a detailed solution to problem 14.

*PROBLEM 15 :*Compute .Click HERE to see a detailed solution to problem 15.

*PROBLEM 16 :*Compute limit (x to -infinity) cos [ x/(x^2+10) + pi/3 ] .Click HERE to see a detailed solution to problem 16.

*PROBLEM 17 :*Compute .Click HERE to see a detailed solution to problem 17.

*PROBLEM 18 :*Compute .Click HERE to see a detailed solution to problem 18.

*PROBLEM 19 :*Compute .Click HERE to see a detailed solution to problem 19.

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

Thu Sep 5 14:47:41 PDT 1996