Chapter 5.2, Problem 14E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

With a programmable calculator or computer (see the instructions for Exercise 5.1.9), compute the left and right Riemann sums for the function *f*(*x*) = *x*/(*x* + 1) on the interval [0, 2] with *n* = 100. Explain why these estimates show that

To determine

**To Calculate:** The left and right Riemann sums for the function

**To Explain**: the reason for the expression of estimate as follows:

Explanation

The value of the function

**Given:**

The function as

The region lies between

Number of rectangles

**Calculation:**

Show the Equation of the function

Calculate the value of the function *x* within the interval

Substitute 0 for *x* in Equation (1).

Substitute 1.5 for *x* in Equation (1).

Substitute 2 for *x* in Equation (1).

The calculated values of *x* shows that the function

The expression to find the left Riemann sum

Here, the left endpoint height of first rectangle is *n*^{th} rectangle is

Find the width

Here, the upper limit is *b*, the lower limit is *a*, and the number of rectangles is *n*.

Substitute 2 for *b*, 0 for *a* and 100 for *n* in Equation (3).

The value of left and right end points within the interval

The left endpoints are

The right endpoints are

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