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Bekki George Lecture notes 10

# Bekki George Lecture notes 10 - Math 1432 Notes Week 10...

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Math 1432 Notes – Week 10 More examples from 10.4 State whether the sequence converges as n ; if it does, find the limit. 1. 7 n e 2. 3. 4.

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5. 6. 7.
8. 9. 9 sin n n π ⎛⎞ ⎜⎟ ⎝⎠ 10. 9 cos( ) nn

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LecPop10_2 1. Give the limit of the sequence: 2 2 13 25 n nn ⎧⎫ ⎨⎬ ++ ⎩⎭ A. 3 1 B. - 3 1 C. 3 D. -3 E. this sequence diverges One more for practice: Determine whether the following sequence converges or diverges. If it converges, find its limit. 2 1: l i m 1 x n n x ar e c a l l e > ⎛⎞ = += ⎜⎟ ⎝⎠
10.5 – The Indeterminant Form (0/0) L’Hopital’s Rule : Suppose that 0 ) ( x f and 0 ) ( x g as + x c x c x c x , , , or −∞ x . If L x g x f ) ( ' ) ( ' then L x g x f ) ( ) ( (Note, it is possible that = or L ) Examples: 1. 2. 0 sin lim x x x > 3.

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4. 2 0 1 lim x x ex x > −− 5. 2 0 1 lim x x e x >
10.6 – The Indeterminant Form ( / ) All Indeterminate forms: L’Hopital’s Rule : Suppose that ± ) ( x f and ± ) ( x g as + x c x c x c x , , , or −∞ x .

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Bekki George Lecture notes 10 - Math 1432 Notes Week 10...

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