   Chapter 13.3, Problem 1E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 1-10, calculate the left Riemann sum for the given function over the given interval, using the given value of n. (When rounding, round answers to four decimal places. If using the tabular method, values of the function in the table should be accurate to at least five decimal places.) [HINT: See Example 2.] f ( x ) = 4 x − 1 over [ 0 ,       2 ] ,     n = 4

To determine

To calculate: The left Riemann sum of the function f(x)=4x1 over the interval [0,2] if, n=4

Explanation

Given Information:

The provided function is f(x)=4x1 and the interval is [0,2]

Formula used:

If a function f is continues then the left Riemann sum of the function f with n equal subdivisions over an interval [a,b] is,

left riemann sum =k=0n1f(xk)Δx=f(x0)Δx+f(x1)Δx+....+f(xn1)Δx=[f(x0)+f(x1)+....f(xn1)]Δx

Where the width of subdivision is Δx=ban and the end points of the subdivisions are a=x0<x1<<xn=b.

Calculation:

Consider a function, f(x)=4x1

Also consider an interval, [0,2] and the value of n, n=4

Compute the width of the subdivisions Δx,

Δx=ban=204=24=0

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