Download presentation
Presentation is loading. Please wait.
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
Find
4
Properties Of Limits Basic - let b and c be real numbers and n be a positive integer Constant Identity Power
5
Properties Of Limits Let L, K, b, and, c be real numbers, let n be a positive integer, and Scalar Multiple: Sum/Difference:
6
Properties Of Limits Let L, K, b, and, c be real numbers, let n be a positive integer, and Power: Product:
7
Properties Of Limits Let L, K, b, and, c be real numbers, let n be a positive integer, and Quotient:
8
Technique 1: Rewrite the function by factoring out Common factors
Find Technique 1: Rewrite the function by factoring out Common factors
9
Technique 2: Rationalize the numerator
Find Technique 2: Rationalize the numerator By multiplying by the complex conjugate
10
Technique 3: Use algebra to rewrite the the function
Find Technique 3: Use algebra to rewrite the the function
11
Strategies for Limits Determine by recognition whether a limit can be evaluated by direct substitution If direct substitution fails, try to use some technique (cancellation, rationalization, or algebraic manipulation) Use a graph or table to verify your conclusion
12
Find
13
Find
14
9) Use and
15
Homework Page 67 # 5 – 25 odd, 37, 38, 39, odd, and assignment 1-3
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.