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1746. Trigonometric substitutions Evaluate the following | Ch 7.4 - 24 |

Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs ISBN: 9780321947345 167

Solution for problem 24 Chapter 7.4

Calculus: Early Transcendentals | 2nd Edition

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Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs

Calculus: Early Transcendentals | 2nd Edition

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Problem 24

1746. Trigonometric substitutions Evaluate the following integrals. L dx 216 + 4x2

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Demand Demand is not linear. P Qd $500 6 $400 16 $300 30 $200 55 $100 60 0 100 ❏ movement from A → B is called an increase in quantity demanded, ​ not an increase in demand ❏ movement from C → D is called a decrease in quantity demanded, ​ not a decrease in demand ❏ only ​ pric can change the amount of quantity demanded ❏ a movement of the ​ entire curv is considered an increase or decrease in demand ● more consumers causes the curve to shift to the right ● less consumers causes the curve to shift to the left Determinants ​(ceteris paribus variables → what changes demand, ​ot pric) 1. population 2. income ○ normal goods → a good whose demand increases because of an increase in income; determined by the individual ○ inferior goods → a good whose demand decreases because of an increase in income; determined by the market Ex: College students buy ramen noodles because they’re cheap. If students have an increase in income, they’d be more likely to buy more mac ‘n’ cheese, which is more expensive. This would cause a decrease in the demand for ramen noodles. In this scenario ramen would be an nferiorgood, and mac ‘n’ cheese would be a normal ​ood. 3. tastes/preferences 4. consumers’ ​ expectations Ex:​ If the government announced they were to increase the sales tax on Mercedes cars in a month, the demand for Mercedes cars would increase in that month because of the expectation that after that month, the car would cost much more. 5. △ (change) in the price of: ○ substitute goods → goods that can be bought in place of another i. absolute price (the price of a good) vs. relative price (the ratio of two prices) Ex:​ If the price of Coke went up, Qd would decrease and some of those consumers would buy a substitute like Pepsi instead. ○ complementary goods → goods that are bought to be used with another Ex:​ If the price of tennis balls increased, people would stretch out the life of their rackets and the demand for rackets would decrease. Supply P Qs $1 0 $5 10 $10 20 $40 50 ❏ movement from A → B is called an increase in quantity supplied​ot an increase in supply ❏ movement from D → C is called a decrease in quantity supplied,​ot a decrease in supply ❏ Consumers want to maximize u ​til​(happiness), producers want to maximize​rofi. ​ ❏ profit ≠ greed ❏ without profits, there would be no production ❏ Law of Supply:​ as price increases – and everything is held constant (ceteris paribus) – quantity supplied increases ❏ producers and consumers rely on each other; they are not enemies ❏ Changes in price do not change demand or supply, they change ​ uantity demanded​and quantity suppli. ​ ❏ a decrease in supply causes the curve to shift to the left ❏ an increase in supply causes the curve to shift to the right Determinants 1. number of suppliers 2. price of inpu (resource) ○ price of labor 3. technology 4. △ price of a related good Ex:If oats turn up a bigger profit, some wheat farmers will switch to oats, causing a decrease in supply. 5. producers’​ expectations Supply and Demand ❏ equilibrium price: one and only price where the quantity supplied is equal to the quantity demanded ❏ “clearing the market” → no surplus, no shortage ❏ consumers’ surplus: paying less than what you’re willing and able to pay ❏ producers’ surplus: selling a product for more than what you’re willing to sell Ex: The equilibrium price is where the supply and demand graphs intersect. The area above the equilibrium price is the consumer surplus, and the area below is the producer surplus. ❏ price ceiling: when the gov’t imposes a max. price a good can be exchanged between buyer and seller, i.e. usury laws (meant to help consumers) Ex:​If the government imposes a price ceiling on apartments lower than the equilibrium price, it would affect the number of quantity demanded and the quantity supplied. ❏ price floor: when the gov’t imposes a min. price producers and consumers can exchange a good (meant to help producers) Ex: Sometimes price floors are placed above the equilibrium price, which would not affect the quantity demanded and supplied for that product. ➢ if supply ncreases​, price decreases and demand increases ➢ if supply ​ecreases​, price increases and demand decreases ➢ if demand i​ncreases, price increases and supply increases ➢ if demand d​ecreases​, price decreases and supply decreases ❏ deadweight/welfare loss: amount left from previous consumers’ & producers’ surplus after a price ceiling/price floor is set

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Chapter 7.4, Problem 24 is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 2
Author: William L. Briggs
ISBN: 9780321947345

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. The full step-by-step solution to problem: 24 from chapter: 7.4 was answered by , our top Calculus solution expert on 12/23/17, 04:24PM. Since the solution to 24 from 7.4 chapter was answered, more than 232 students have viewed the full step-by-step answer. The answer to “1746. Trigonometric substitutions Evaluate the following integrals. L dx 216 + 4x2” is broken down into a number of easy to follow steps, and 12 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. This full solution covers the following key subjects: . This expansive textbook survival guide covers 128 chapters, and 9720 solutions.

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1746. Trigonometric substitutions Evaluate the following | Ch 7.4 - 24 |