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Section 1.2

Section 1.2. Finding Limits Graphically and Numerically. What is a limit?. Finding limits numerically. F(x) = (x 2 – 3x + 2)/(x – 2). Finding limits graphically:. Finding limits:. Find. Limits that fail to exist:. 1). Limits that fail to exist:. 2) 3). Limits that fail to exist:.

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Section 1.2

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  1. Section 1.2 Finding Limits Graphically and Numerically

  2. What is a limit?

  3. Finding limits numerically. F(x) = (x2 – 3x + 2)/(x – 2)

  4. Finding limits graphically:

  5. Finding limits: Find

  6. Limits that fail to exist: 1)

  7. Limits that fail to exist: 2) 3)

  8. Limits that fail to exist: 4)

  9. A formal definition of a limit • If f(x) becomes arbitrarily close to a single number L as x approaches c from either side than . • For each ε > , there exists a > such that if 0 < | x- c| < , then |f(x) – L| < ε

  10. Finding a for a given ε • Find . Then find > 0 such that |f(x) – L| < 0.01 whenever 0 < |x – c| <

  11. Using the definition of a limit • Prove • Prove =-1

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