16 Use Theorems 9.9 and 9.10 or Exercises 9.9-9.15 to prove the following: (a) lim nª+8n n² +9 (b) lim[+(-1)"] = +∞ (c) lim[32 321=+m = +∞

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10th Edition
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Chapter2: Second-order Linear Odes
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THEOREM 9.10 For a sequence (sn) of positive real numbers, we have lim sn = +∞ if and only if lim(1/sn ) = 0.

THEOREM 9.9 

Let (sn) and (tn) be sequences such that lim sn = +∞ and lim tn > 0 [lim tn can be finite or +∞]. Then lim sntn = +∞.

9.16 Use Theorems 9.9 and 9.10 or Exercises 9.9-9.15 to prove the following:
(a) lim n¹+8n
n²+9
= +∞
(b) lim[2/2 + (−1)″] = +∞
3
(c) lim[³
= +m
Transcribed Image Text:9.16 Use Theorems 9.9 and 9.10 or Exercises 9.9-9.15 to prove the following: (a) lim n¹+8n n²+9 = +∞ (b) lim[2/2 + (−1)″] = +∞ 3 (c) lim[³ = +m
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