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Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
Textbook Problem

At a temperature of 20°C, the volume V(in liters) of 1.33 g of O2 is related to its pressure p (in atmospheres) by the formula V = 1/p.

  1. a. What is the average rate of change of V with respect to p as p increases from p = 2 to p = 3?
  2. b. What is the rate of change of V with respect to p when p = 2?

(a)

To determine

To find: The average rate of change of V (volume) with respect to p(pressure) as pressure increases from p=2 to p=3 .

Explanation

Given:

The given formula which relates the volume V (in liters) of the 1.33g of O2 to its pressure P at 20°C is,

V=1p (1)

Formula used:

The formula to calculate the average change in volume with respect to p (pressure) over the interval [p,p+h] is,

Averagerateofchange=RateofchangeinvolumeRateofchangeinpressure=V(p+h)V(p)(p+h)p (2)

Calculation:

For given interval [2,3] value of p is 2 and value of (p+h) is 3, for the average rate of change of volume first compute V(3) and V(2) .

Substitute 3 for p in equation (1) to calculate the value of V(3) ,

V(3)=13 .

Substitute 2 for p in equation (1) to calculate the value of V(2) ,

V(2)=12

(b)

To determine

To find: The rate of change of volume at p=2 .

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