DID YOU A Subscribe to Remind Text kphscalbc
DID YOU… A. Subscribe to Remind? Text @kphscalbc to 81010 B. Bring the necessary supplies? If so, would you please leave it on the desk and I will collect it. C. For today, pick up some notes in the back of the room D. Fill out the information page (“All About Me”) yet? If not, please complete it by Monday. It is available online at dangmath. com 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 1
EVALUATING LIMITS ANALYTICALLY Section 1. 3 Calculus BC AP/Dual, Revised © 2017 viet. dang@humbleisd. net 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 2
EASY LIMITS 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 3
EXAMPLE 1 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 4
EXAMPLE 2 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 5
EXAMPLE 3 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 6
REVIEW OF COMPOSITIONS 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 7
REVIEW EXAMPLE A 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 8
REVIEW EXAMPLE B 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 9
EXAMPLE 4 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 10
YOUR TURN 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 11
PROPERTIES OF LIMITS 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 12
EXAMPLE 5 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 13
EXAMPLE 6 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 14
EXAMPLE 7 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 15
EXAMPLE 8 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 16
YOUR TURN 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 17
12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 18
EXAMPLE 9 What form is this? 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 19
EXAMPLE 9 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 20
EXAMPLE 10 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 21
WHEN IN ALGEBRA… You learned to: NO RADICALS IN THE DENOMINATOR FOR LIMITS, NO RADICALS IN THE NUMERATOR OR DENOMINATOR 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 22
EXAMPLE 11 What form is this? 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 23
EXAMPLE 11 NO NEED TO FOIL THE BOTTOM 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 24
EXAMPLE 11 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 25
YOUR TURN 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 26
EXAMPLE 12 What form is this? 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 27
EXAMPLE 12 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 28
EXAMPLE 12 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 29
EXAMPLE 12 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 30
EXAMPLE 13 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 31
YOUR TURN 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 32
“SQUEEZE THEOREM” 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 33
“SQUEEZE THEOREM” 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 34
EXAMPLE 14 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 35
EXAMPLE 14 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 36
EXAMPLE 15 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 37
YOUR TURN 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 38
SPECIAL TRIGONOMETRIC LIMITS 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 39
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EXAMPLE 16 Split the fraction up so we can isolate and utilize a trigonometric limit 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 42
EXAMPLE 16 Utilize the Product Property of Limits 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 43
EXAMPLE 17 Try to convert it to one of its trig limits. Try to get it where the sine trig function to cancel. Whatever is applied to the bottom, must be applied to the top. 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 44
EXAMPLE 17 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 45
EXAMPLE 18 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 46
YOUR TURN 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 47
PATTERN? 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 48
EXAMPLE 19 Split the fraction up so we can isolate and utilize a trigonometric limit 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 49
EXAMPLE 19 cos(0) = 1 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 50
YOUR TURN 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 51
AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 52
AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) Vocabulary 12/15/2021 1: 50 AM Connections and Process § 1. 3: Properties of Limits with Trigonometry Answer and Justifications 53
ASSIGNMENT Page 67 5 -21 EOO, 23, 25, 27 -35 odd, 37 -57 odd (omit 45), 63 -73 odd, 89 12/15/2021 1: 50 AM § 1. 3: Properties of Limits with Trigonometry 54
- Slides: 54