Calculus With Precalculus Section 34 Continuity and Onesided Limits Answers

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ONE-SIDED LIMITS AND CONTINUITY Section 1. 4 Calculus BC AP/Dual, Revised © 2016 viet. [email protected] k 12. tx. us 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 1

REVIEW 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 2

ONE–SIDED LIMITS 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 3

IDENTIFY ONE–SIDED LIMITS LEFT SIDE RIGHT SIDE 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 4

EXAMPLE 1 2 1 3 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 5

EXAMPLE 2 2 1 3 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 6

YOUR TURN 3 2 1 3 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 5 7

CONTINUITY ON AN OPEN INTERVAL 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 8

DISCONTINUITY EXAMPLES A. Removable Discontinuity (You can fill the hole in and continue with the function on the right and left side) B. Non-removable discontinuity 1. Jump 2. Infinite 3. Oscillating 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 9

EXAMPLE 3 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 10

EXAMPLE 4 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 11

YOUR TURN 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 12

EXAMPLE 5 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 13

EXAMPLE 6 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 14

YOUR TURN 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 15

PIECEWISE FUNCTION LIMITS A. Compare the extremes of the piecewise function B. Take the right side of the top extreme and equal it to the left side of the middle equation to establish the gap C. Solve for the variable D. Repeat process for second variable 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 16

EXAMPLE 7 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 17

EXAMPLE 8 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 18

YOUR TURN 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 19

CONTINUITY ON A CLOSED INTERVAL 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 20

CONTINUITY ON A CLOSED INTERVAL 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 21

EXAMPLE 9 1 – 1 1/25/2022 3: 41 PM 0 1. 4: One-Sided Limits and Continuity BC 22

EXAMPLE 10 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 23

YOUR TURN 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 24

DEFINITION OF CONTINUITY 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 25

EXAMPLES OF DISCONTINUOUS 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 26

PROPERTIES OF CONTINUITY 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 27

EXAMPLE 11 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 28

EXAMPLE 11 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 29

EXAMPLE 12 1/25/2022 3: 41 PM 1. 4: One-Sided Limits and Continuity BC 30

EXAMPLE 12 1/25/2022 3: 42 PM 1. 4: One-Sided Limits and Continuity BC 31

EXAMPLE 13 1/25/2022 3: 42 PM 1. 4: One-Sided Limits and Continuity BC 32

EXAMPLE 13 1/25/2022 3: 42 PM 1. 4: One-Sided Limits and Continuity BC 33

EXAMPLE 14 1/25/2022 3: 42 PM 1. 4: One-Sided Limits and Continuity BC 34

EXAMPLE 15 1/25/2022 3: 42 PM 1. 4: One-Sided Limits and Continuity BC 35

YOUR TURN 1/25/2022 3: 42 PM 1. 4: One-Sided Limits and Continuity BC 36

EXAMPLE 16 1/25/2022 3: 42 PM 1. 4: One-Sided Limits and Continuity BC 37

EXAMPLE 16 1/25/2022 3: 42 PM 1. 4: One-Sided Limits and Continuity BC 38

YOUR TURN 1/25/2022 3: 42 PM 1. 4: One-Sided Limits and Continuity BC 39

ASSIGNMENT Page 78 1 -13 EOO, 19 -25 odd, 27 -51 EOO, 53, 61 -65 odd 1/25/2022 3: 42 PM 1. 4: One-Sided Limits and Continuity BC 40

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Source: https://slidetodoc.com/onesided-limits-and-continuity-section-1-4-calculus/

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