Two-sided limits using algebra

The  exercise appears under the Precalculus Math Mission and Differential calculus Math Mission. This exercise explores calculating limits with some algebra manipulation.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the limit using algebra: This problem has a limit of a rational function approaching an integer. The student is expected to find the limit and write the correct answer in the space provided.Tslua1.png

Strategies
Knowledge of the evaluating functions and factoring quadratics are encouraged to ensure success on this exercise.
 * 1) The first method for solving a limit is to plug in the limiting value for x. If this is defined, the result is the answer.
 * 2) The second method for solving limits on this exercise is to factor the numerator and denominator, reduce, and then plug in. The result will be the answer.
 * 3) L'hopital's rule comes later in the standard calculus sequence, but after introduced it can be used to perform this exercise more efficiently.

Real-life Applications

 * 1) Limits are the foundation for both differential and integral calculus.
 * 2) The concept of continuity is rigorously defined via limits.
 * 3) Asymptotes of rational functions can be understood more rigorously by looking at them as limits.