The left endpoints, right endpoints, and midpoints of the four subintervals are:
Left endpoints: [-4, -2, 0, 2]
Right endpoints: [-2, 0, 2, 4]
Midpoints: [-3, -1, 1, 3]
Dividing the interval [-4, 4] into n = 4 equal subintervals means creating four subintervals of equal width. To find the width of each subinterval, we can use the formula:
width = (b - a) / n
where:
width is the width of each subinterval
a is the left endpoint of the interval
b is the right endpoint of the interval
n is the number of subintervals
In this case, we have:
a = -4
b = 4
n = 4
Plugging these values into the formula, we get:
width = (4 - (-4)) / 4 = 2
Therefore, each subinterval has a width of 2.
To find the left and right endpoints of each subinterval, we can start at the left endpoint of the interval (-4) and add the width of each subinterval repeatedly. This gives us the following left endpoints:
-4, -2, 0, 2
To find the right endpoints of each subinterval, we simply add the width of each subinterval to the corresponding left endpoint. This gives us the following right endpoints:
-2, 0, 2, 4
Finally, to find the midpoint of each subinterval, we can average the left and right endpoints. This gives us the following midpoints:
-3, -1, 1, 3
Therefore, the left endpoints, right endpoints, and midpoints of the four subintervals are:
Left endpoints: [-4, -2, 0, 2]
Right endpoints: [-2, 0, 2, 4]
Midpoints: [-3, -1, 1, 3]
Question
suppose the interval [-4,4]is divided into n=4 equal subintervals. what are the right endpoints, left endpoints, and midpoints of these intervals?