SECTION 2.4 Continuity & One-Sided Limits. Discontinuous v. Continuous.

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Presentation transcript:

SECTION 2.4 Continuity & One-Sided Limits

Discontinuous v. Continuous

Formal Definition of Continuity Definition of Continuity (p. 90)

Two Types of Discontinuity

One-Sided Limits

When Does a Limit Exist? Theorem 2.10 The Existence of a Limit (p. 93)

Example 1 (#6)

Calculating One-Sided Limits 1. Plug in the x-value that you are approaching. 2. If you get a real number, then that’s your limit. 3. If not, try some algebra to see if things can cancel. 4. If that doesn’t work, then plug in x-values extremely close to the number you are approaching or graph it.

Example 2

Example 2 (cont.)

Continuity on a Closed Interval Definition of Continuity on a Closed Interval (p. 93)

Pictorial Representation

Example 3

Example 4

Example 5

Example 5 (cont.)

SECTION 2.5 Infinite Limits

Infinite Limits Defined

A Picture: An Example:

Infinite Limits

Vertical Asymptotes

Example 1

Example 2

Example 3

Example 4