A sequence is an infinite ordered list of numbers that is often defined by a fun

Question

A sequence is an infinite ordered list of numbers that is often defined by a function. For example, the sequence {2,4, 6, S, middot middot middot } is specified by the function f(n) = 2n, where n = 1,2, 3, middot middot middot. The limit of such a sequence is limn rightarrow infin f(n), provided the limit exists. All limit laws for limits at infinity may be applied to limits of sequences. Find the limit of the following sequence. {3,1,5 / 9, 3 / 8, middot middot middot middot}, which is defined by f(n) = n +2 / n2for n = 1,2,3, middot middot middot The limit of the sequence is . Find the limit of the following sequence, or state that the limit does not exist. {2, 3 / 4, 4 / 9, 5 / 16, middot middot middot}, which is defined by f(n) = n + 1 / n2 for n = 1,2,3... Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The limit exists, lim n rightarrow infin f(n) = (Simplify your answer.) The limit does not exist. If a function f represents a system that varies with time, the existence of lim t rightarrow infin f(t) means that the system reaches a steady state (or equilibrium). If the amplitude of an oscillator is given by a(t) = 6(t + sin t / t), determine if a steady state exists and give the steady-state value. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A steady state exists and the steady-state value is . A steady state does not exist.

Explanation / Answer

Limit=0

A Limit exists and=0

A steady state exists and value is 6

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