Day29-1432class - 3 x x x →∞ = 5 lim 2 x x x e →∞ =...

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Math 1432 Think: Look at each of the following words, there is a connection between them. What is it? TIMBER BENCH LIZARD SAMPLE EMCF 7. ABABB DDACB 8. ABABD ABAAA 9. CCCCC DBAEC 10. CCBDA EBABB 11. BBAAA FAAAD 12. DDDDD DDDDD 13. ABAAA BDCAC
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Section 10.5 The Indeterminate Form (0/0) Section 10.6 The Indeterminate Form ( / ) and others
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The forms 0 0 and are called indeterminate because they do not guarantee that a limit exists, nor do they indicate what the limit is, if one does exist. ( 29( 29 lim lim lim 2 4 x 0 4 2 x 0 x 2 3x 5x 5x 6x x 2 x 2 x 2 = = - + = -
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Previously you tried different methods to find the indicated limits: 1. lim 2 x 1 2x 2 x 1 →- - = + 2. lim 2 2 x 3x 1 2x 1 →∞ - = + 3. lim x 7 x 2 3 x 7 + - = -
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Now………..
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Indeterminate form 1. lim 3x x 0 e 1 x - = 2. sin lim 3 x 0 x x x - = 0 0
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3. lim x 7 x 2 3 x 7 + - = - 4. cos lim 2 4 x 0 2 x 2 x x - + =
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5. sin lim sin x 0 2x 3x = 6. arcsin lim x 0 x x =
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Indeterminate form 1. lim 2 2 x 5x 3x 3x 1 →∞ - = + 2. ln lim x x x →∞ =
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3. ln lim 5 x x x →∞ = 4. ( 29 ln lim 3 x x x →∞ =
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5. lim
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Unformatted text preview: 3 x x x →∞ = 5. lim 2 x x x e →∞ = 6. lim x 2 x x 1 →∞ = + 7. ( 29 tan lim ln x 1 x 2 x 1 + → π =-8. lim x x e x →∞ = lim , a x x x a 0 e →∞ = ln lim , a x x a 0 x →∞ = Other Indeterminate forms. 1 ∞ ∞ • ∞ ∞ - ∞ The first three arise from limits of functions that have variable bases and variable exponents. Rewrite. 1. lim x x e x-→∞ = 2. ( 29 lim ln x x x + →-= • ∞ 3. lim sin x 1 x x →∞ = 1 ∞ 1. lim x x 1 1 x →∞ + = 2. ( 29 lim 1 x x 1 x + → + = These are all indeterminate. These are “determinate”. ∞-∞ ∞ + ∞ → ∞-∞ - ∞ → -∞ → → ∞ 1 ∞ ∞ ∞ • ∞ ∞ - ∞ ∞ POPPER Assignment 23 People Soft #...
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