1. For each function below, determine whether it is discrete or not. Then, explain your choice.(6.7)(-2.4)(a, 5)a)Discrete? Y / NExplanation:b) Infinite and Finite SequencesYou may have noticed in 1b of the practice problems, that sequence had a . behind it. This means that thesequence continues on, and if there is a pattern to that sequence, it does so following that pattern. Fromthis, we can make the two following statements:1. A sequence that has no last term, but continues on indefinitely is an infinite sequence.2. A sequence that has a last term is a finite sequence.Here we encounter a problem. What if we wanted to write out an entire infinite sequence? By its verydefinition, it would take us forever to do it! Take the sequence:Clearly, if we kept counting, we could guess the next numbers on our list: 10, 12, 14, 16, etc. but since thesequence goes on forever, we require a shorter way of writing it all out. After all, what if someone asked usto find the 10 term in that sequence? We could just keep adding +2 until we reached it, but that's a lot ofunnecessary work.Instead, if we figure out what rule / pattern the sequence follows as it goes from one term to the next, wecan come up with what is called a general term. The general term can be written out as t, where n can beany number.Ex. 1 Find the general term for the sequence 3, 6, 9, 12, .To find the general term, let's first see if we can recognize a pattern:Term NumberTerm ValueS(n) or t,1.3212It looks like whatever our term number is, we can always multiply it by 3 to get out term value. Therefore,the "rule" we're looking for is . If we write that out as an equation, then we get:Let's test this rule out. According to the list above, the third number is 9, meaning when, should equalUsing our formula from above, we can substitute 3 for n, and if our math is right, we should get 9 back:+ Based on this, our "rule" is correct.Ex. 2 Find the general term for the sequence 1, 8, 27, 64,..Again, to find the general term let's first see if we can recognize a pattern by asking ourselves what we cando to "n" in order to change it into "t.":Term NumberTerm ValueS(n) or t,32764It seems like we can take any of our n values, raise them to the exponent 3, and then get back a t, value. Forinstance, 2' = 8 and 4' = 64. Therefore, our "rule" is:

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Answered: 1. For each function below, determine…

1. For each function below, determine whether it is discrete or not. Then, explain your choice. (-2.4) (a) a) Discrete? Y /N Explanation:

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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