Limit calculations. For each real-valued sequence, explain whether it is convergent, divergent to ±0, or otherwise divergent (not to too). If it is convergent, find its limit. If it is divergent, find its lim sup and lim inf. 23 - 1 n° (a) lim n∞ 1-3n3 (b) lim x n³ - - 2 - 2

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Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "oo" (without the quotation marks). If it diverges to negative infinity, state your answer as "-oo". If it diverges without being infinity or negative infinity, state your answer as "DNE". 6 - 4n + 9" lim n- 00

Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. (If it diverges to infinity, state your answer as inf . If it diverges to negative infinity, state your answer as -inf . If it diverges without being infinity or negative infinity, state your answer as div .) 12(5") + 17 lim 11(2") Answer:

Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "o0" (without the quotation marks). If it diverges to negative infinity, state your answer as "-o0". If it diverges without being infinity or negative infinity, state your answer as "DNE". n2 lim 2 00 e

Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "oo" (without the quotation marks). If it diverges to negative infinity, state your answer as "-o0". If it diverges without being infinity or negative infinity, state your answer as "DNE". n" lim n+ 00 e4n

Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "oo" (without the quotation marks). If it diverges to negative infinity, state your answer as "-oo". If it diverges without being infinity or negative infinity, state your answer as "DNE". lim n→∞ n4 - 6n e

Determine if the sequence {a} converges or diverges. Find the limit if the sequence converges. (-1)^+1 5n-9 an = Select the correct choice below and fill in any answer boxes within your choice. OA. The sequence {a} converges. The limit is lim an = n→∞ OB. The sequence {an} diverges. (Simplify your answer.)

Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as INF. If it diverges to negative infinity, state your answer as MINF. If it diverges without being infinity or negative infinity, state your answer as DIV. lim n→∞ 6(n!) (-8)n

Calculations. For each sequence, explain whether it is conver- gent, divergent to ±∞, or otherwise divergent (not to ±∞). If it is convergent, find its limit. Don't use L'Hopital.