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Sequences part 2
Another sequence worksheet to go with the first one:
Calculus I Exploration, Sequences and Limits, part II
The following exercise is designed to arrive at rules for determining long-term behavior directly from a sequence generator function without building a table.
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Make a hypothesis about the long-term behavior of sequences generated by the difference equation xn+1=λxn, x0. Try to come up with some generalizations: sequences that look like _____ will do _____ long-term. You may have several hypotheses, depending on the values of xn, x0, and λ.
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Test at least one other example for each hypothesis formed. Does it agree, disagree? If it disagrees, go back to step 1. When it agrees, move to step 3 for each hypothesis.
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Create a written argument that explains why the general hypothesis is true. You may use an example to illustrate, but it must be a general explanation for any example that would fall in that case.
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Create a comprehensive, yet minimal list of “rules” and explanations derived in 1-3. Cut and paste into the text box provided under the assignment link on Canvas.
Your blog assignment:
Record your observations from this exploration. Also write down your resulting minimal list of hypotheses with verbal justifications about why they are true.
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