Question

Let rn denote the left-endpoint sum using n subintervals. compute the indicated left sum for the given function on the indicated interval. (round your answer to four decimal places.) r6 for f(x)=(1)/(x(x-1)) on [2, 5]

Answer 1

To calculate the left-endpoint sum r6 for f(x) = 1/(x(x-1)) on [2, 5], six subintervals are used and the function is evaluated at each left endpoint, then each value is multiplied by the width of the subintervals to get the sum.

Step-by-step explanation:

To compute the left-endpoint sum r6 for the function f(x) = 1/(x(x-1)) on the interval [2, 5], we need to divide the interval into n subintervals. Since we are using 6 subintervals (n=6), each subinterval will have a width of (5-2)/6 which is 0.5. The left endpoints for these subintervals are 2, 2.5, 3, 3.5, 4, and 4.5.

Next, we evaluate the function at each left endpoint:

• f(2) = 1/(2*1) = 0.5
• f(2.5) = 1/(2.5*1.5)
• f(3) = 1/(3*2)
• f(3.5) = 1/(3.5*2.5)
• f(4) = 1/(4*3)
• f(4.5) = 1/(4.5*3.5)

The left-endpoint sum r6 is the sum of the function values at these points multiplied by the width of the subintervals:

r6 = 0.5 * (f(2) + f(2.5) + f(3) + f(3.5) + f(4) + f(4.5))

Calculating this sum and rounding to four decimal places gives us the final result.