Question

Let Ln denote the left-endpoint sum using n subintervals and let Rn denote the corresponding right-endpoint sum. In the following exercise, compute the indicated left and right sums for the given function on the indicated interval.
L4 for f(x)=1/x−1; [2,3]

Answer 1

Answer:

$L_4=0.7595$

Step-by-step explanation:

We are given that

$f(x)=\frac{1}{x-1},$[2,3]

We have to find L4

It means n=4

$\Delta x=\frac{b-a}{n}=\frac{3-2}{4}=\frac{1}{4}=0.25$

Now, intervals are

[2,2.25],[2.25,2.50],[2.5,2.75],[2.75,3]

Now,

$L_4=f(x_0)\Delta x+f(x_1)\Delta x+f(x_2)\Delta x+f(x_3)\Delta x$

$L_4=\frac{1}{2-1}(0.25)+\frac{1}{2.25-1}(0.25)+\frac{1}{2.5-1}(0.25)+\frac{1}{2.75-1}(0.25)$

$L_4=0.7595$