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Single Variable Calculus

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781305266636

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BuyFindarrow_forward

Single Variable Calculus

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781305266636
Chapter 8.4, Problem 5E
Textbook Problem
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A demand curve is given by p = 450/(x + 8). Find the consumer surplus when the selling price is $10.

To determine

To calculate: The consumer surplus when the selling price is $10.

Explanation of Solution

Given information:

The equation of demand curve is p(x)=450(x+8).

Selling price is p=$10.

Calculation:

Show the demand function as follows:

p(x)=450(x+8) (1)

Substitute $10 for p(x) in Equation (1).

10=450(x+8)x+8=45x=37

Substitute 0 for x in Equation (1).

p(0)=450(0+8)=56.25

Sketch the region for the calculated values and identify the consumer surplus as shown in Figure 1.

Refer to Figure 1.

The shaded area denoted as consumer surplus.

Find the consumer surplus as shown below.

Consumersurplus=0x(p(x)p)dx (2)

Substitute 37 for x, 450(x+8) for p(x), and $10 for p in Equation (2)

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Chapter 8 Solutions

Single Variable Calculus
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Ch. 8.1 - Find the exact length of the curve. 11....Ch. 8.1 - Find the exact length of the curve. 12....Ch. 8.1 - Find the exact length of the curve. 13....Ch. 8.1 - Find the exact length of the curve. 14. y = ln(cos...Ch. 8.1 - Find the exact length of the curve. 15. y = ln(sec...Ch. 8.1 - Find the exact length of the curve. 16....Ch. 8.1 - Find the exact length of the curve. 17....Ch. 8.1 - Find the exact length of the curve. 18....Ch. 8.1 - Find the exact length of the curve. 19....Ch. 8.1 - Find the exact length of the curve. 20. y = 1 ex,...Ch. 8.1 - Find the length of the arc of the curve from point...Ch. 8.1 - Find the length of the arc of the curve from point...Ch. 8.1 - Graph the curve and visually estimate its length....Ch. 8.1 - Graph the curve and visually estimate its length....Ch. 8.1 - Use Simpsons Rule with n = 10 to estimate the arc...Ch. 8.1 - Use Simpsons Rule with n = 10 to estimate the arc...Ch. 8.1 - Use Simpsons Rule with n = 10 to estimate the arc...Ch. 8.1 - Use Simpsons Rule with n = 10 to estimate the arc...Ch. 8.1 - (a) Graph the curve y=x4x3,0x4. 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