   Chapter 13.8, Problem 25E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 23-30, round all calculations to 2 decimal places.Cost Suppose that a company’s total cost (in dollars) of producing x items is given by C ( x ) = ( x 2 + 1 ) 3 / 2 +   1000 . Use the Trapezoidal Rule with n = 3 to approximate the average total cost for the production of x = 30 to x = 33 items.

To determine

To calculate: The average total cost for the production of x=30 to x=33 items using Trapezoidal Rule with n=3 if a company’s total cost (in dollars) of producing x items is given by C(x)=(x2+1)32+1000.

Explanation

Given Information:

A company’s total cost of producing x items is given by

C(x)=(x2+1)32+1000

Formula Used:

As per the Trapezoidal Rule:

If f is continuous on [a,b], then,

abf(x)dxh2[f(x0)+2f(x1)+2f(x2)+2f(x3)++2f(xn2)+2f(xn1)+f(xn)]

Where h=ban and n is the number of equal subdivisions of [a,b].

Calculation:

The provided expression is C(x)=(x2+1)32+1000,

In order to apply the rule, the value of h is as follows:

h=33303=33=1

Hence, the value of h is 1.

So, the interval [30,33] is divided into 3 subintervals as follows,

Put the values of the xi's in the equation

abf(x)dxh2[f(x0)+2f(x1)+2f(x2)+2f(x3)++2f(xn2)+2f(xn1

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