Is Induction Proof Needed for this Limit Problem?

In summary, the problem is to prove that for a fixed positive real number s, the limit of e^-sN (s sin bN + b cos bN) as N approaches infinity is equal to 0. This problem was mentioned in a chapter on Laplace Transforms and it has been determined that proof by induction is not applicable. The rules for the homework forum require the use of a template and showing work up to the point of being stuck.
  • #1
Alex13S
2
0
Prove that for fixed s > 0, we have

lim e^-sN ( s sin bN + b cos bN ) = 0
N ->

This problem was in a chapter on Laplace Transforms. I'm assuming this will require proof by induction.
 
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  • #2
Induction is used when you want to prove one statement P(n) for each positive integer n. Here you want to prove one statement P(s) for each positive real number s, so induction is of no use.

You should take a look at the rules for the homework forum before the next time you start a thread. In particular, you are required to use the template and to show us your work up to the point where you're stuck.
 
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FAQ: Is Induction Proof Needed for this Limit Problem?

1. What is an induction proof problem?

An induction proof problem is a mathematical problem that is solved using the method of mathematical induction. This method involves proving that a statement is true for a base case, and then showing that if the statement is true for any given case, it must also be true for the next case. This process is repeated until the statement is proven to be true for all possible cases.

2. How is mathematical induction used to solve problems?

Mathematical induction is used to prove that a statement is true for all cases in a specific set. This method involves proving a base case and then using the inductive hypothesis, which states that if the statement is true for any given case, it must also be true for the next case. This process is repeated until the statement is proven to be true for all cases in the set.

3. What is the base case in an induction proof problem?

The base case in an induction proof problem is the starting point for the proof. It is the first case that is used to prove that a statement is true. In most cases, the base case is the smallest or simplest case in the set being considered.

4. How do you know when to use mathematical induction?

Mathematical induction is useful when trying to prove a statement for all cases in a specific set. It is commonly used in mathematics and computer science to prove theorems and statements about sequences, series, and other mathematical structures. In general, if a problem involves proving a statement for all cases in a set, mathematical induction is a good method to use.

5. Can mathematical induction be used to solve any problem?

No, mathematical induction cannot be used to solve all problems. It is only useful when trying to prove a statement for all cases in a specific set. If a problem does not involve proving a statement for all cases, another method of proof may be more appropriate. Additionally, some problems may be too complex to be solved using mathematical induction, and other proof techniques may be needed.

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