Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![Suppose that
• The Demand Price Function is p = D(x) = 120 -0.02x.
• The selling price has been established as p
=
60.
The goal is to find the value of the Consumers' Surplus (CS) by two methods.
Method 1 (Using Geometry) Do the following:
a. For the selling price p 60, find the corresponding Demand, x.
b. Graph the Demand Price Function D(x). What is the domain of this function? Why?
c. Plot the point (x,p) on the graph of the Demand Price Function that you just made.
d. Shade the region corresponding to the Consumers' Surplus.
e. Use a simple geometric formula for area to find the area of the region that you shaded on your graph. This is the Consumers' Surplus, computed using Geometry.
Method 2 (Using Calculus) Do the following:
f. Set up the definite integral that calculates the Consumers' Surplus. That is, set up the integral
x
√ [D(x) − p]dx
g. Find the value of the Consumers' Surplus by evaluating the definite integral that you set up in part (f). This is the Consumers' Surplus, computed using Calculus.
CS=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9258546b-0cd2-4d03-b6f3-ed5967c2726b%2F7d049658-6c63-4e88-a929-77689ac09c40%2Fpkjeb2_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that
• The Demand Price Function is p = D(x) = 120 -0.02x.
• The selling price has been established as p
=
60.
The goal is to find the value of the Consumers' Surplus (CS) by two methods.
Method 1 (Using Geometry) Do the following:
a. For the selling price p 60, find the corresponding Demand, x.
b. Graph the Demand Price Function D(x). What is the domain of this function? Why?
c. Plot the point (x,p) on the graph of the Demand Price Function that you just made.
d. Shade the region corresponding to the Consumers' Surplus.
e. Use a simple geometric formula for area to find the area of the region that you shaded on your graph. This is the Consumers' Surplus, computed using Geometry.
Method 2 (Using Calculus) Do the following:
f. Set up the definite integral that calculates the Consumers' Surplus. That is, set up the integral
x
√ [D(x) − p]dx
g. Find the value of the Consumers' Surplus by evaluating the definite integral that you set up in part (f). This is the Consumers' Surplus, computed using Calculus.
CS=
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