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Use the appropriate limit laws and theorems to determine the limit of the sequence. An= n/5 Sin(4/n)

User Glenn Moss
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To determine the limit of the sequence A(n) = n/5 * sin(4/n) as n approaches infinity, we can use the limit laws and theorems.

First, let's simplify the expression:

A(n) = (n/5) * sin(4/n)

As n approaches infinity, we have:

lim(n→∞) (n/5) = ∞/5 = ∞

Now, let's examine the term sin(4/n) as n approaches infinity:

lim(n→∞) sin(4/n) = sin(0) = 0

Using the limit laws, we can now find the limit of the sequence:

lim(n→∞) A(n) = lim(n→∞) [(n/5) * sin(4/n)]
= lim(n→∞) (n/5) * lim(n→∞) sin(4/n)
= ∞ * 0
= 0

Therefore, the limit of the sequence A(n) = n/5 * sin(4/n) as n approaches infinity is 0.
User TheTXI
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