Calculate the 5-unit moving average of the function
f(x) = x^2/3
over what interval?
and is that (x^2)/3 or x^(2/3)?
To calculate the 5-unit moving average of a function, you need to take the average value of the function over a 5-unit interval. This involves summing the values of the function over that interval and dividing by the number of units in the interval.
In this case, we have the function f(x) = x^(2/3). To find the 5-unit moving average, we will calculate the average value of the function over each 5-unit interval.
Let's start by choosing a starting point for the 5-unit interval. For simplicity, let's choose x = 0 as our starting point. We will calculate the average value of the function over the interval from x = 0 to x = 5.
To do this, we need to evaluate the function at each point within the interval, sum the values, and divide by the number of units (in this case, 5).
Let's calculate the values of f(x) within the interval:
f(0) = (0)^(2/3) = 0
f(1) = (1)^(2/3) = 1
f(2) = (2)^(2/3) = 1.587
f(3) = (3)^(2/3) = 2.080
f(4) = (4)^(2/3) = 2.519
f(5) = (5)^(2/3) = 2.924
Now let's sum these values:
0 + 1 + 1.587 + 2.080 + 2.519 + 2.924 = 10.110
Finally, divide the sum by the number of units (5) to find the moving average:
10.110 / 5 = 2.022
Therefore, the 5-unit moving average of the function f(x) = x^(2/3) over the interval from x = 0 to x = 5 is approximately 2.022.