Problem 1 - Calculus Early Transcendentals

Question

If the interval [4,18] is partitioned into \(n=28\) sub-intervals of equal length, what is \(\Delta x ?\)

Step-by-Step Solution

Answer

Answer: The length of each sub-interval when the interval [4,18] is partitioned into 28 equal parts is Δx = 1/2.

Step 1: Determine the length of the interval

Calculate the total length of the interval by subtracting the lower limit from the upper limit. In this case, the interval is [4,18]. So, the length of the interval is \(18 - 4 = 14.\)

Step 2: Divide the length by the number of partitions

Next, we need to partition the interval into 28 equal parts. To find the length of each part, we will divide the total length by the number of partitions. In this case, the total length is 14, and the number of partitions is 28. Therefore, the length of each partition or sub-interval is \(\frac{14}{28}.\)

Step 3: Simplify the fraction

Now, we will simplify the fraction \(\frac{14}{28}.\) Dividing the numerator and denominator by their greatest common divisor, which is 14, we get \(\frac{1}{2}.\)

Step 4: Write the answer

Finally, the length of each sub-interval is \(\Delta x = \frac{1}{2}.\)