1. Finding Limits Using Tables and Graphs
Section 14.1
Finding Limits Using Tables and Graphs
and
Section 14.2
Algebra Techniques for Finding Limits

2. Objectives
Find a limit using a table.
Find a limit using a graph.
Find the limit of a sum, a difference, and a product.
Find the limit of a polynomial.
Find the limit of a power or a root.
Find the limit of a quotient.

3. LIMIT

8. Notice that the value at 0, that is, f(0) = 0, plays no role in finding the limit. In fact, even if f were undefined at 0, it would still have a limit there in this case.

9. As x gets closer to 0 from above, the function approaches 0, but as x gets closer to 0 from below, the function stays at 2, so the limit does not exist.

12. The book lists several theorems (sum, difference, product, quotient, …). The bottom line is that if direct substitution works, use it!

22. If we try to use the quotient property we find the limit of the denominator is 0 so we cannot use this formula. We see however, that both the numerator and denominator factor and we can reduce.

23. The quotient rule cannot be used because the denominator is 0
The quotient rule cannot be used because the denominator is 0. We see however, that both the numerator and denominator factor and we can reduce.

24. Homework
14.1 #7 (table: 1.9, 1.99, 1.999, 2, 2.001, 2.01, 2.1), #11 (table: 3.9, 3.99, 3.999, 4, 4.001, 4.01, 4.1),
#17, 19, 21
14.2 #15-35 odd