1.2 Finding Limits Graphically and Numerically

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Sec. 1.2: Finding Limits Graphically and Numerically.

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Presentation transcript:

1.2 Finding Limits Graphically and Numerically

Objectives Study and use a formal definition of a limit.

An Informal Definition of a Limit c - δ c c + δ DeltaEpsilonDemo

ε-δ Definition of a Limit Cauchy gave us the standard ε-δ definition of a limit "f(x) becomes arbitrarily close to L" The distance between f and L is less than some really, really small value ε. "as x approaches c." The distance between x and c is less than some really small value of δ.

Formal Definition of a Limit Let f be a function defined on an open interval containing c (except possibly at c), and let L be a real number. The statement means that for each ε>0, there exists a δ>0 such that if You determine how close (accurate) you want L to be to f (and how small ε is) and you find a δ that makes that happen.

Example

Example

Example

Homework 1.2 (page 56) #39, 43, 45 Answers: 39. L=8 43. L=6 45. L=-3