Question

Let Ln 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.) L4 for f(x) = 1/x-1on [3, 4] L4 =

Answer 1

The indicated left sum for the given function on the indicated interval, the value L4 for f(x) = 1/x-1on [3, 4] L4 = 0.7595.

Let Ln denote the left-endpoint sum using n sub intervals.

We are given that

$f(x) = \frac{1}{x-1}$  [3,4]

We have to find L4

It means n = 4

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

Now, intervals are

[3, 3.25], [3.25, 3.50], [3.5, 3.75], [3.75, 4]

Now,

$L_{4} = f(x_{0}) \triangle x+f(x_{1})\triangle x +f(x_{2})\triangle x+f(x_{3})\triangle x\\ \\ L_{4} = \frac{1}{3-1} (0.25)+\frac{1}{3.25-1}(0.25)+\frac{1}{3.5-1}(0.25)+\frac{1}{3.75-1}(0.25)\\ \\ L_{4} = 0.7595$

Hence the answer is the indicated left sum for the given function on the indicated interval, the value L4 for f(x) = 1/x-1on [3, 4] L4 = 0.7595.

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