Method(s) to determine the growth rate of a function or sequence
In mathematics, we often say that a particular function of sequence has a growth or decay rate. For example, we say the value, or terms, grow or decay at a linear, polynomial, exponential, logarithmic, or some other rate.
My question is this: Given a function or sequence, what are the methods for determining and showing its rate of growth or decay?
Additionally, if you have a function or sequence which is the sum or product of other functions and sequences with particular growth or decay rates, what are the rules for how these combine to produce the rate for the composite function of sequence?
For example, suppose I have the integer sequence:
$a_n = n^n times exp(n), nin mathbb{N}$
What is the best method to determine what the growth rate is for sequence?
sequences-and-series analysis
asked Nov 30 at 1:41
jdg
12
add a comment |
In mathematics, we often say that a particular function of sequence has a growth or decay rate. For example, we say the value, or terms, grow or decay at a linear, polynomial, exponential, logarithmic, or some other rate.
My question is this: Given a function or sequence, what are the methods for determining and showing its rate of growth or decay?
Additionally, if you have a function or sequence which is the sum or product of other functions and sequences with particular growth or decay rates, what are the rules for how these combine to produce the rate for the composite function of sequence?
For example, suppose I have the integer sequence:
$a_n = n^n times exp(n), nin mathbb{N}$
What is the best method to determine what the growth rate is for sequence?
sequences-and-series analysis
asked Nov 30 at 1:41
jdg
12
Big O notation can be used to give a description of the growth rate: en.wikipedia.org/wiki/Big_O_notation
– parsiad
Nov 30 at 1:44
add a comment |
In mathematics, we often say that a particular function of sequence has a growth or decay rate. For example, we say the value, or terms, grow or decay at a linear, polynomial, exponential, logarithmic, or some other rate.
My question is this: Given a function or sequence, what are the methods for determining and showing its rate of growth or decay?
Additionally, if you have a function or sequence which is the sum or product of other functions and sequences with particular growth or decay rates, what are the rules for how these combine to produce the rate for the composite function of sequence?
For example, suppose I have the integer sequence:
$a_n = n^n times exp(n), nin mathbb{N}$
What is the best method to determine what the growth rate is for sequence?
sequences-and-series analysis
asked Nov 30 at 1:41
jdg
12
In mathematics, we often say that a particular function of sequence has a growth or decay rate. For example, we say the value, or terms, grow or decay at a linear, polynomial, exponential, logarithmic, or some other rate.
My question is this: Given a function or sequence, what are the methods for determining and showing its rate of growth or decay?
Additionally, if you have a function or sequence which is the sum or product of other functions and sequences with particular growth or decay rates, what are the rules for how these combine to produce the rate for the composite function of sequence?
For example, suppose I have the integer sequence:
$a_n = n^n times exp(n), nin mathbb{N}$
What is the best method to determine what the growth rate is for sequence?
sequences-and-series analysis
sequences-and-series analysis
asked Nov 30 at 1:41
jdg
12
asked Nov 30 at 1:41
jdg
12
asked Nov 30 at 1:41
jdg
12
asked Nov 30 at 1:41
jdg
12
asked Nov 30 at 1:41
jdg
12
12
Big O notation can be used to give a description of the growth rate: en.wikipedia.org/wiki/Big_O_notation
– parsiad
Nov 30 at 1:44
add a comment |
Big O notation can be used to give a description of the growth rate: en.wikipedia.org/wiki/Big_O_notation
– parsiad
Nov 30 at 1:44
Big O notation can be used to give a description of the growth rate: en.wikipedia.org/wiki/Big_O_notation
– parsiad
Nov 30 at 1:44
Big O notation can be used to give a description of the growth rate: en.wikipedia.org/wiki/Big_O_notation
– parsiad
Nov 30 at 1:44
add a comment |
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Big O notation can be used to give a description of the growth rate: en.wikipedia.org/wiki/Big_O_notation
– parsiad
Nov 30 at 1:44