DIRECT AND LIMIT COMPARISON TEST Section 9 4

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DIRECT AND LIMIT COMPARISON TEST Section 9. 4 Calculus BC AP/Dual, Revised © 2018

DIRECT AND LIMIT COMPARISON TEST Section 9. 4 Calculus BC AP/Dual, Revised © 2018 viet. dang@humbleisd. net 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests 1

SUMMARY OF TESTS FOR SERIES 12/25/2021 8: 20 PM § 9. 4: Direct and

SUMMARY OF TESTS FOR SERIES 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests 2

ANALOGY: SCENARIO 1 Anna 12/25/2021 8: 20 PM Brian § 9. 4: Direct and

ANALOGY: SCENARIO 1 Anna 12/25/2021 8: 20 PM Brian § 9. 4: Direct and Limit Comparison Tests 3

ANALOGY: SCENARIO 2 Anna 12/25/2021 8: 20 PM Brian § 9. 4: Direct and

ANALOGY: SCENARIO 2 Anna 12/25/2021 8: 20 PM Brian § 9. 4: Direct and Limit Comparison Tests 4

ANALOGY: SCENARIO 3 Anna 12/25/2021 8: 20 PM Brian § 9. 4: Direct and

ANALOGY: SCENARIO 3 Anna 12/25/2021 8: 20 PM Brian § 9. 4: Direct and Limit Comparison Tests 5

ANALOGY Anna 12/25/2021 8: 20 PM Brian § 9. 4: Direct and Limit Comparison

ANALOGY Anna 12/25/2021 8: 20 PM Brian § 9. 4: Direct and Limit Comparison Tests 6

ANALOGY 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests 7

ANALOGY 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests 7

DIRECT COMPARISON TEST 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison

DIRECT COMPARISON TEST 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests 8

DIRECT COMPARISON TEST 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison

DIRECT COMPARISON TEST 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests 9

DIRECT COMPARISON TEST 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison

DIRECT COMPARISON TEST 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests 10

STEPS FOR DIRECT COMPARISON TEST 12/25/2021 8: 20 PM § 9. 4: Direct and

STEPS FOR DIRECT COMPARISON TEST 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests 11

EXAMPLE 1 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests

EXAMPLE 1 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests 12

EXAMPLE 1 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests

EXAMPLE 1 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests 13

EXAMPLE 1 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests

EXAMPLE 1 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests 14

EXAMPLE 2 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests

EXAMPLE 2 12/25/2021 8: 20 PM § 9. 4: Direct and Limit Comparison Tests 15

EXAMPLE 2 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

EXAMPLE 2 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 16

EXAMPLE 2 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

EXAMPLE 2 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 17

YOUR TURN 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

YOUR TURN 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 18

YOUR TURN 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

YOUR TURN 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 19

EXAMPLE 3 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

EXAMPLE 3 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 20

EXAMPLE 3 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

EXAMPLE 3 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 21

EXAMPLE 3 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

EXAMPLE 3 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 22

EXAMPLE 4 Harmonic series 12/25/2021 8: 21 PM § 9. 4: Direct and Limit

EXAMPLE 4 Harmonic series 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 23

YOUR TURN 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

YOUR TURN 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 24

YOUR TURN 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

YOUR TURN 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 25

YOUR TURN 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

YOUR TURN 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 26

REVIEW EXAMPLE 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

REVIEW EXAMPLE 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 27

REVIEW EXAMPLE 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

REVIEW EXAMPLE 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 28

LIMIT COMPARISON TEST 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison

LIMIT COMPARISON TEST 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 29

STEPS FOR LIMIT COMPARISON TEST 12/25/2021 8: 21 PM § 9. 4: Direct and

STEPS FOR LIMIT COMPARISON TEST 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 30

EXAMPLE 4 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

EXAMPLE 4 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 31

EXAMPLE 4 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

EXAMPLE 4 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 32

EXAMPLE 4 The answer is positive and finite. 12/25/2021 8: 21 PM § 9.

EXAMPLE 4 The answer is positive and finite. 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 33

EXAMPLE 5 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

EXAMPLE 5 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 34

EXAMPLE 5 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

EXAMPLE 5 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 35

EXAMPLE 5 Solve using L’Hospital’s Rule 12/25/2021 8: 21 PM § 9. 4: Direct

EXAMPLE 5 Solve using L’Hospital’s Rule 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests The answer is positive and finite. 36

EXAMPLE 6 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests

EXAMPLE 6 12/25/2021 8: 21 PM § 9. 4: Direct and Limit Comparison Tests 37

EXAMPLE 6 12/25/2021 8: 22 PM § 9. 4: Direct and Limit Comparison Tests

EXAMPLE 6 12/25/2021 8: 22 PM § 9. 4: Direct and Limit Comparison Tests 38

EXAMPLE 6 The answer is positive and finite. 12/25/2021 8: 22 PM § 9.

EXAMPLE 6 The answer is positive and finite. 12/25/2021 8: 22 PM § 9. 4: Direct and Limit Comparison Tests 39

YOUR TURN 12/25/2021 8: 22 PM § 9. 4: Direct and Limit Comparison Tests

YOUR TURN 12/25/2021 8: 22 PM § 9. 4: Direct and Limit Comparison Tests 40

YOUR TURN 12/25/2021 8: 22 PM § 9. 4: Direct and Limit Comparison Tests

YOUR TURN 12/25/2021 8: 22 PM § 9. 4: Direct and Limit Comparison Tests 41

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) 12/25/2021 8: 22 PM § 9. 4:

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) 12/25/2021 8: 22 PM § 9. 4: Direct and Limit Comparison Tests 42

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) Vocabulary 12/25/2021 8: 22 PM Connections and

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) Vocabulary 12/25/2021 8: 22 PM Connections and Process § 9. 4: Direct and Limit Comparison Tests Answer 43

AP MULTIPLE CHOICE PRACTICE QUESTION 2 (NON-CALCULATOR) 12/25/2021 8: 22 PM § 9. 4:

AP MULTIPLE CHOICE PRACTICE QUESTION 2 (NON-CALCULATOR) 12/25/2021 8: 22 PM § 9. 4: Direct and Limit Comparison Tests 44

AP MULTIPLE CHOICE PRACTICE QUESTION 2 (NON-CALCULATOR) Vocabulary 12/25/2021 8: 22 PM Connections and

AP MULTIPLE CHOICE PRACTICE QUESTION 2 (NON-CALCULATOR) Vocabulary 12/25/2021 8: 22 PM Connections and Process § 9. 4: Direct and Limit Comparison Tests Answer 45

ASSIGNMENT Page 616 3 -23 odd, 23 -30 all, 33 -41 odd 12/25/2021 8:

ASSIGNMENT Page 616 3 -23 odd, 23 -30 all, 33 -41 odd 12/25/2021 8: 22 PM § 9. 4: Direct and Limit Comparison Tests 46