Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1. For each function below, determine whether it is discrete or not. Then, explain your choice. (-2.4) (a) a) Discrete? Y /N Explanation:

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
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 / N Explanation: b)
Transcribed Image Text: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 / N Explanation: b)
Infinite and Finite Sequences You may have noticed in 1b of the practice problems, that sequence had a . behind it. This means that the sequence continues on, and if there is a pattern to that sequence, it does so following that pattern. From this, 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 very definition, 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 the sequence goes on forever, we require a shorter way of writing it all out. After all, what if someone asked us to find the 10 term in that sequence? We could just keep adding +2 until we reached it, but that's a lot of unnecessary work. Instead, if we figure out what rule / pattern the sequence follows as it goes from one term to the next, we can come up with what is called a general term. The general term can be written out as t, where n can be any 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 Number Term Value S(n) or t, 1. 3 2 12 It 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 equal Using 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 can do to "n" in order to change it into "t.": Term Number Term Value S(n) or t, 3 27 64 It seems like we can take any of our n values, raise them to the exponent 3, and then get back a t, value. For instance, 2' = 8 and 4' = 64. Therefore, our "rule" is:
Transcribed Image Text:Infinite and Finite Sequences You may have noticed in 1b of the practice problems, that sequence had a . behind it. This means that the sequence continues on, and if there is a pattern to that sequence, it does so following that pattern. From this, 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 very definition, 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 the sequence goes on forever, we require a shorter way of writing it all out. After all, what if someone asked us to find the 10 term in that sequence? We could just keep adding +2 until we reached it, but that's a lot of unnecessary work. Instead, if we figure out what rule / pattern the sequence follows as it goes from one term to the next, we can come up with what is called a general term. The general term can be written out as t, where n can be any 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 Number Term Value S(n) or t, 1. 3 2 12 It 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 equal Using 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 can do to "n" in order to change it into "t.": Term Number Term Value S(n) or t, 3 27 64 It seems like we can take any of our n values, raise them to the exponent 3, and then get back a t, value. For instance, 2' = 8 and 4' = 64. Therefore, our "rule" is:
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS