This

**preview**shows pages 1-3. to view the full**11 pages of the document.**Limits and Derivatives

2.1 The Tangent and Velocity Problems

Limits arise when we attempt to find the tangent to a curve or the

velocity of an object.

2.2 The Limit of a Function

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o It is easy to guess the wrong value if we use inappropriate

values of , but it is difficult to know when to stop calculating

values.

o Sometimes calculators and computers give the wrong values.

One-sided limits

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Infinite limits

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o Another example of a function whose graph has a vertical

asymptote is the natural logarithmic function

2.3 Calculating Limits Using the Limit Laws

Laws:

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2.4 The Precise Definition of a Limit

Definition

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o It can be expressed in words as

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Infinite Limits

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