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1.4 Continuity and One-Sided Limits (Part 1)

1.4 Continuity and One-Sided Limits (Part 1). Objectives. Determine one-sided limits and continuity on a closed interval. One-Sided Limits. Example. Two-Sided Limits. For most rational & polynomial functions: no difference in left, right or two-sided limits Need to check both sides if:

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1.4 Continuity and One-Sided Limits (Part 1)

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  1. 1.4 Continuity and One-Sided Limits(Part 1)

  2. Objectives • Determine one-sided limits and continuity on a closed interval.

  3. One-Sided Limits

  4. Example

  5. Two-Sided Limits • For most rational & polynomial functions: no difference in left, right or two-sided limits • Need to check both sides if: • Even radical (domain gap) • Piecewise functions • Absolute value • Infinite Limits (next section)

  6. Example For even radicals, evaluate the domain first. D: x-2≥0, x≥2 [2,∞)

  7. Example D: 1-x2≥0, x2≤1, |x|≤1, [-1,1]

  8. Examples Show domain on test!

  9. Example

  10. Example

  11. Greatest Integer Function

  12. Examples

  13. Homework 1.4 (page 76) #1-7 odd, #11-17 odd #21,23 Handout (2.5) #1-9 odd #21, 22, 24, 30, 44, 48, 49, 50, 52

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