1. 1.3 EVALUATING LIMITS ANALYTICALLY

2. Direct Substitution If the the value of c is contained in the domain (the function exists at c) then Direct Substitution is valid for ALL polynomials and rational functions with non-zero denominators

3. 1) Find 2) Find

4. Properties Of Limits Basic - let b and c be real numbers and n be a positive integer I. Constant II. Identity III. Power

5. Properties Of Limits Let L, K, b, and, c be real numbers, let n be a positive integer, and 1. Scalar Multiple: 2. Sum/Difference:

6. Properties Of Limits Let L, K, b, and, c be real numbers, let n be a positive integer, and 3. Power: 4. Product:

7. Properties Of Limits Let L, K, b, and, c be real numbers, let n be a positive integer, and 5. Quotient:

8. 3) Find Technique 1: Rewrite the function by factoring out Common factors

9. 4) Find Technique 2: Rationalize the numerator By multiplying by the complex conjugate

10. 5) Find Technique 3: Use algebra to rewrite the the function

11. Strategies for Limits 1)Determine by recognition whether a limit can be evaluated by direct substitution 2)If direct substitution fails, try to use some technique (cancellation, rationalization, or algebraic manipulation) 3)Use a graph or table to verify your conclusion

12. 6)Find 7)Find

13. 8)Find

14. 9) Use and

15. Homework Page 67 # 5 – 25 odd, 37, 38, 39, 41-57 odd,