Is a general sequence possible for the given data?

In summary, for an assignment in Analysis, the conversation discusses exploring a family of functions and determining the highest order derivative that exists and its continuity. The pattern of k and n, where k is a positive integer and n is the highest order derivative, is mentioned and the possibility of generalizing it as a sequence is brought up. Finally, the question of whether n=floor((k-1)/2) would work is asked and answered positively.
  • #1
SithsNGiggles
186
0
I finished exploring a family of functions

fk(x) = {xksin(1/x) for x≠0
{0 for x=0
for an assignment in my Analysis course, and I'm supposed to determine the highest order derivative that exists and whether or not it's continuous.

I've noticed a pattern:
k = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...}
n = {0, 0, 1, 1, 2, 2, 3, 3, 4, 4, ...},
where k is a positive integer, and n is the highest order derivative that exists.

I want to save some space on my page by generalizing these results as a sequence. Is this possible, and if so what's the sequence? Thanks.
 
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  • #2
Would n=floor((k-1)/2) work?
 
  • #3
Char. Limit said:
Would n=floor((k-1)/2) work?

Yes, I figured it out very recently. Thank you.
 

Related to Is a general sequence possible for the given data?

1. What is a general sequence?

A general sequence is a mathematical concept that refers to a pattern of numbers or objects that follow a specific rule or formula. It is a way of organizing data to help identify patterns and make predictions about future values.

2. How is a general sequence different from a specific sequence?

A specific sequence is a set of numbers or objects that follow a specific pattern, while a general sequence is a more abstract concept that encompasses all possible patterns and rules that can be applied to a given set of data. A specific sequence is a subset of a general sequence.

3. What are some examples of a general sequence?

Examples of a general sequence include arithmetic sequences (where each term increases or decreases by a fixed amount), geometric sequences (where each term is a multiple of the previous term), and Fibonacci sequences (where each term is the sum of the two previous terms).

4. How do you determine if a general sequence is possible for a given set of data?

To determine if a general sequence is possible for a given set of data, you need to look for patterns and relationships between the data points. This can be done by plotting the data points on a graph and observing the trend. If there is a clear pattern or rule that can be applied to the data, then a general sequence is possible.

5. Why is it important to study general sequences?

Studying general sequences is important because it allows us to understand and predict patterns in data, which can be useful in various fields such as mathematics, science, and economics. It also helps us develop critical thinking skills and problem-solving abilities.

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