CALCULUS AND ITS APPLICATIONS BRIEF
CALCULUS AND ITS APPLICATIONS BRIEF
12th Edition
ISBN: 9780135998229
Author: BITTINGER
Publisher: PEARSON
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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Chapter 2.3, Problem 34E

a.

To determine

To find: The value t12,000 and t′12,000 .

b.

To determine

To find: The population of flies.

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Chapter 2 Solutions

CALCULUS AND ITS APPLICATIONS BRIEF

Ch. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Graph each function. Then identify the domain,...Ch. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10ECh. 2.1 - For Exercises 9-16, an initial investment amount...Ch. 2.1 - Prob. 12E
Ch. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.1 - For Exercises 9-16, an initial investment amount...Ch. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - For Exercises 17-26, use a calculator to find each...Ch. 2.1 - Prob. 22ECh. 2.1 - For Exercises 17-26, use a calculator to find each...Ch. 2.1 - Prob. 24ECh. 2.1 - For Exercises 17-26, use a calculator to find each...Ch. 2.1 - Prob. 26ECh. 2.1 - Given ln4=1.3863 and ln5=1.6094, use properties of...Ch. 2.1 - Prob. 28ECh. 2.1 - Given ln4=1.3863 and ln5=1.6094, use properties of...Ch. 2.1 - Prob. 30ECh. 2.1 - Given ln4=1.3863 and ln5=1.6094, use properties of...Ch. 2.1 - Prob. 32ECh. 2.1 - Given ln4=1.3863 and ln5=1.6094, use properties of...Ch. 2.1 - Prob. 34ECh. 2.1 - Given ln4=1.3863 and ln5=1.6094, use properties of...Ch. 2.1 - Prob. 36ECh. 2.1 - Given ln4=1.3863 and ln5=1.6094, use properties of...Ch. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Solve for t. Round the answer to three decimal...Ch. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - Prob. 48ECh. 2.1 - Solve for t. Round the answer to three decimal...Ch. 2.1 - Prob. 50ECh. 2.1 - Prob. 51ECh. 2.1 - Prob. 52ECh. 2.1 - Find the domain of each logarithmic function and...Ch. 2.1 - Prob. 54ECh. 2.1 - Find the domain of each logarithmic function and...Ch. 2.1 - Prob. 56ECh. 2.1 - Find the domain of each logarithmic function and...Ch. 2.1 - Prob. 58ECh. 2.1 - Prob. 59ECh. 2.1 - Prob. 60ECh. 2.1 - Prob. 61ECh. 2.1 - Prob. 62ECh. 2.1 - Solve each logarithmic equation. Round the answer...Ch. 2.1 - Prob. 64ECh. 2.1 - Prob. 65ECh. 2.1 - Prob. 66ECh. 2.1 - Solve each logarithmic equation. Round the answer...Ch. 2.1 - Prob. 68ECh. 2.1 - U.S. travel exports. U.S. travel exports (goods...Ch. 2.1 - Prob. 70ECh. 2.1 - Compound interest: future value. Dennis deposits...Ch. 2.1 - Prob. 72ECh. 2.1 - Prob. 73ECh. 2.1 - Prob. 74ECh. 2.1 - Prob. 75ECh. 2.1 - Prob. 76ECh. 2.1 - Prob. 77ECh. 2.1 - Prob. 78ECh. 2.1 - Prob. 79ECh. 2.1 - Prob. 80ECh. 2.1 - Cooling liquid. A cup of hot coffee is placed on a...Ch. 2.1 - Prob. 82ECh. 2.1 - Prob. 83ECh. 2.1 - Prob. 84ECh. 2.1 - In Exercises 8594, solve for x. 85. e2x5ex+4=0....Ch. 2.1 - Prob. 86ECh. 2.1 - Prob. 87ECh. 2.1 - Prob. 88ECh. 2.1 - In Exercises 8594, solve for x. 89. e2xex12=0Ch. 2.1 - Prob. 90ECh. 2.1 - Prob. 91ECh. 2.1 - Prob. 92ECh. 2.1 - Prob. 93ECh. 2.1 - Prob. 94ECh. 2.1 - Prob. 95ECh. 2.1 - Prob. 96ECh. 2.1 - Prob. 97ECh. 2.1 - Prob. 99ECh. 2.1 - Prob. 100ECh. 2.1 - Prob. 101ECh. 2.1 - Prob. 102ECh. 2.1 - Prob. 103ECh. 2.2 - Differentiate. 1. g(x)=e2xCh. 2.2 - Prob. 2ECh. 2.2 - Differentiate. 3. g(x)=3e5xCh. 2.2 - Prob. 4ECh. 2.2 - Differentiate. 5. G(x)=x35e2xCh. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Differentiate. 11. f(x)=x22x+2exCh. 2.2 - Prob. 12ECh. 2.2 - Differentiate. 13. f(x)=ex2+8xCh. 2.2 - Prob. 14ECh. 2.2 - Differentiate. 15. y=ex1Ch. 2.2 - Prob. 16ECh. 2.2 - Differentiate. 17. y=ex+x3xexCh. 2.2 - Prob. 18ECh. 2.2 - Differentiate. 19. g(x)=4x2+3xex27xCh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Differentiate. 23. r(t)=t2+2tet2Ch. 2.2 - Differentiate. 24. f(t)=t35te4t3Ch. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Find the second derivative. 31. d(x)=e2x+1Ch. 2.2 - Prob. 32ECh. 2.2 - Prob. 33ECh. 2.2 - Prob. 34ECh. 2.2 - Find the second derivative. 35. w(x)=xexCh. 2.2 - Prob. 36ECh. 2.2 - Find the second derivative. 37. f(t)=(2t+3)e3tCh. 2.2 - Prob. 38ECh. 2.2 - Find the second derivative. 39. z(x)=e2x+12Ch. 2.2 - Prob. 40ECh. 2.2 - Find the second derivative. 41. w(t)=t2+2t+3e5tCh. 2.2 - Prob. 42ECh. 2.2 - Prob. 43ECh. 2.2 - Prob. 44ECh. 2.2 - Find the second derivative. 45. f(t)=e3t1Ch. 2.2 - Prob. 46ECh. 2.2 - Marginal cost. The total cost, in millions of...Ch. 2.2 - Prob. 48ECh. 2.2 - Growth of a retirement fund. Maria invests $20,000...Ch. 2.2 - Prob. 50ECh. 2.2 - Depreciation. Perriots Restaurant purchased...Ch. 2.2 - Prob. 52ECh. 2.2 - Prob. 53ECh. 2.2 - Prob. 54ECh. 2.2 - Prob. 59ECh. 2.2 - Prob. 60ECh. 2.2 - Prob. 61ECh. 2.2 - Prob. 62ECh. 2.2 - Prob. 63ECh. 2.2 - Prob. 64ECh. 2.2 - Prob. 65ECh. 2.2 - Prob. 66ECh. 2.2 - Prob. 67ECh. 2.2 - Prob. 68ECh. 2.2 - Prob. 69ECh. 2.2 - Prob. 70ECh. 2.2 - Prob. 71ECh. 2.2 - Prob. 72ECh. 2.2 - For each of the functions in Exercises 70-73,...Ch. 2.2 - Prob. 75ECh. 2.3 - Differentiate. 1. y=9lnxCh. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Differentiate. 5. fx=ln10xCh. 2.3 - Prob. 6ECh. 2.3 - Differentiate. 7. y=x6lnxCh. 2.3 - Prob. 8ECh. 2.3 - Differentiate. 9. y=lnxx5Ch. 2.3 - Prob. 10ECh. 2.3 - Differentiate. 11. y=lnx24Hint:lnAB=lnAlnBCh. 2.3 - Prob. 12ECh. 2.3 - Differentiate. 13. y=ln3x2+2x1Ch. 2.3 - Differentiate. 14. y=ln7x2+5x+2Ch. 2.3 - Differentiate. 15. f(x)=lnx2+5xCh. 2.3 - Differentiate. 16. f(x)=lnx27xCh. 2.3 - Differentiate. 17. g(x)=(lnx)4 (Hint: Use the...Ch. 2.3 - Differentiate. 18. g(x)=(lnx)3Ch. 2.3 - Differentiate. 19. h(x)=lnx2x3+1e2xCh. 2.3 - Differentiate. 20. h(x)=ln2x4e3xx2+x+15Ch. 2.3 - Find the equation of the line tangent to the graph...Ch. 2.3 - Find the equation of the line tangent to the graph...Ch. 2.3 - Find the equation of the line tangent to the graph...Ch. 2.3 - Find the equation of the line tangent to the graph...Ch. 2.3 - Prob. 25ECh. 2.3 - Advertising. A model for consumers' response to...Ch. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Forgetting. As part of a study, students in a...Ch. 2.3 - Walking speed. Bornstein and Bornstein found in a...Ch. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 36ECh. 2.3 - Prob. 37ECh. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - In Exercise 34, the time t, in weeks, needed for...Ch. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Let y1=ax and y2=lnx. Find a such that the graph...Ch. 2.3 - Prob. 46ECh. 2.4 - Find f if f(x)=4f(x).Ch. 2.4 - Find g if g(x)=6g(x).Ch. 2.4 - Find the function that satisfies dA/dt=9A.Ch. 2.4 - Find the function that satisfies dP/dt=3P(t).Ch. 2.4 - Find the function that satisfies dQ/dt=kQ.Ch. 2.4 - Find the function that satisfies dR/dt=kR.Ch. 2.4 - U.S. patents. Between 2006 and 2016, the number of...Ch. 2.4 - Franchise expansion. Pete Zah's, Inc., is selling...Ch. 2.4 - Compound interest. If an amount P0 is invested in...Ch. 2.4 - Compound interest. If an amount P0 is deposited in...Ch. 2.4 - Bottled water sales. The volume of bottled water...Ch. 2.4 - Apps downloads. Since June 2014, the number of...Ch. 2.4 - Art masterpieces. In 2004, a collector paid...Ch. 2.4 - Prob. 14ECh. 2.4 - Federal receipts. In 2013, U.S. federal receipts...Ch. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Value of Manhattan Island. Peter Minuit of the...Ch. 2.4 - Total revenue. Intel, a computer chip...Ch. 2.4 - The U.S. Forever Stamp. The U.S. Postal Service...Ch. 2.4 - Prob. 22ECh. 2.4 - Effect of advertising. Suppose that SpryBorg Inc....Ch. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Limited population growth: Human Population....Ch. 2.4 - Prob. 30ECh. 2.4 - 44. Limited population growth. A lake is stocked...Ch. 2.4 - Prob. 32ECh. 2.4 - Hullian learning model. The Hullian learning model...Ch. 2.4 - Spread of infection. Spread by skin-to-skin...Ch. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - We have now studied models for linear, quadratic,...Ch. 2.4 - We have now studied models for linear, quadratic,...Ch. 2.4 - We have now studied models for linear, quadratic,...Ch. 2.4 - We have now studied models for linear, quadratic,...Ch. 2.4 - We have now studied models for linear, quadratic,...Ch. 2.4 - We have now studied models for linear, quadratic,...Ch. 2.4 - We have now studied models for linear, quadratic,...Ch. 2.4 - We have now studied models for linear, quadratic,...Ch. 2.4 - We have now studied models for linear, quadratic,...Ch. 2.4 - We have now studied models for linear, quadratic,...Ch. 2.4 - We have now studied models for linear, quadratic,...Ch. 2.4 - Prob. 48ECh. 2.4 - Prob. 49ECh. 2.4 - Prob. 50ECh. 2.4 - Prob. 51ECh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Prob. 10ECh. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Population decay. The population of Cortez Breaks...Ch. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Radioactive decay. For Exercises 23-26, complete...Ch. 2.5 - Radioactive decay. For Exercises 23-26, complete...Ch. 2.5 - Carbon dating. How old is an ivory tusk that has...Ch. 2.5 - Carbon dating. How old is a piece of wood that has...Ch. 2.5 - 21. Cancer Treatment. Iodine-125 is often used to...Ch. 2.5 - Carbon dating. How old is a Chinese artifact that...Ch. 2.5 - Prob. 33ECh. 2.5 - Present value. Following the birth of a child, a...Ch. 2.5 - Present value. Following the birth of their child,...Ch. 2.5 - Present value. Desmond wants to have $15,000...Ch. 2.5 - 27. Sports salaries. An athlete signs a contract...Ch. 2.5 - 28. Actor’s salaries. An actor signs a film...Ch. 2.5 - Prob. 39ECh. 2.5 - Prob. 40ECh. 2.5 - Salvage value. Lucas Mining estimates that the...Ch. 2.5 - Prob. 42ECh. 2.5 - Prob. 43ECh. 2.5 - Prob. 47ECh. 2.5 - Prob. 48ECh. 2.5 - Prob. 49ECh. 2.5 - 37. Decline in beef consumption. Annual...Ch. 2.5 - Prob. 51ECh. 2.5 - Prob. 52ECh. 2.5 - 40. Cooling. After warming the water in a hot tub...Ch. 2.5 - 41. Cooling. The temperature in a whirlpool bath...Ch. 2.5 - Forensics. A coroner arrives at a murder scene at...Ch. 2.5 - 43. Forensics. A coroner arrives at 11 p.m. She...Ch. 2.5 - Prisoner-of-war protest. The initial weight of a...Ch. 2.5 - 45. Political Protest. A monk weighing 170 lb...Ch. 2.5 - 46. Atmospheric Pressure. Atmospheric pressure P...Ch. 2.5 - 47. Satellite power. The power supply of a...Ch. 2.5 - Prob. 61ECh. 2.5 - For each of the scatterplots in Exercise 49-58,...Ch. 2.5 - Prob. 63ECh. 2.5 - Prob. 64ECh. 2.5 - Prob. 65ECh. 2.5 - Prob. 66ECh. 2.5 - For each of the scatterplots in Exercise 49-58,...Ch. 2.5 - Prob. 68ECh. 2.5 - Prob. 69ECh. 2.5 - For each of the scatterplots in Exercise 49-58,...Ch. 2.5 - Prob. 71ECh. 2.5 - A sample of an element lost 25% of its mass in 5...Ch. 2.5 - 60. A vehicle lost 15% of its value in 2 yr....Ch. 2.5 - The Beer-Lambert Law. A beam of light enters a...Ch. 2.5 - The Beer-Lambert Law. A beam of light enters a...Ch. 2.5 - Prob. 76ECh. 2.5 - An interest rate decreases from 8% to 7.2%....Ch. 2.5 - Prob. 78ECh. 2.6 - Prob. 1ECh. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Prob. 4ECh. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - In Exercises 1-12, find an exponential function of...Ch. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Prob. 12ECh. 2.6 - Differentiate. 1. Ch. 2.6 - Differentiate. y=7xCh. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Prob. 17ECh. 2.6 - Prob. 18ECh. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - Differentiate. y=7x4+2Ch. 2.6 - Differentiate. 8. Ch. 2.6 - Differentiate. 23. f(t)=100(0.52)tCh. 2.6 - Prob. 24ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Prob. 29ECh. 2.6 - Prob. 30ECh. 2.6 - Differentiate. 31. y=5log6x2+xCh. 2.6 - Prob. 32ECh. 2.6 - Prob. 33ECh. 2.6 - Prob. 34ECh. 2.6 - Prob. 35ECh. 2.6 - Prob. 36ECh. 2.6 - Prob. 37ECh. 2.6 - Prob. 38ECh. 2.6 - Prob. 39ECh. 2.6 - Prob. 40ECh. 2.6 - Prob. 41ECh. 2.6 - Prob. 42ECh. 2.6 - Prob. 43ECh. 2.6 - Prob. 44ECh. 2.6 - Prob. 45ECh. 2.6 - Prob. 46ECh. 2.6 - Prob. 47ECh. 2.6 - Prob. 48ECh. 2.6 - Prob. 49ECh. 2.6 - Prob. 50ECh. 2.6 - Recycling glass. In 2012,34.1 of all glass...Ch. 2.6 - Prob. 52ECh. 2.6 - Prob. 53ECh. 2.6 - Prob. 54ECh. 2.6 - Prob. 55ECh. 2.6 - Prob. 56ECh. 2.6 - Prob. 57ECh. 2.6 - Prob. 58ECh. 2.6 - Prob. 59ECh. 2.6 - Prob. 60ECh. 2.6 - A population P0 doubles every 5yr. Find the...Ch. 2.6 - Prob. 62ECh. 2.6 - Prob. 63ECh. 2.6 - Prob. 64ECh. 2.6 - Prob. 65ECh. 2.6 - Prob. 66ECh. 2.6 - Prob. 67ECh. 2.6 - Prob. 68ECh. 2 - Prob. 1RECh. 2 - In Exercises 1-6, match each equation in column A...Ch. 2 - In Exercises 1-6, match each equation in column A...Ch. 2 - Prob. 4RECh. 2 - In Exercises 1-6, match each equation in column A...Ch. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Prob. 31RECh. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - Prob. 35RECh. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - Business: price of a prime-rib dinner. Suppose the...Ch. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Prob. 49RECh. 2 - Prob. 50RECh. 2 - Prob. 52RECh. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Prob. 55RECh. 2 - Prob. 56RECh. 2 - Prob. 57RECh. 2 - Prob. 58RECh. 2 - Differentiate. y=2e3xCh. 2 - Differentiate. y=(lnx)4Ch. 2 - Differentiate. 3. Ch. 2 - Differentiate. f(x)=lnx7Ch. 2 - Differentiate. 5. Ch. 2 - Differentiate. f(x)=3exlnxCh. 2 - Differentiate. 7. Ch. 2 - Prob. 8TCh. 2 - Prob. 9TCh. 2 - Prob. 10TCh. 2 - Prob. 11TCh. 2 - Prob. 12TCh. 2 - Prob. 13TCh. 2 - Prob. 15TCh. 2 - Prob. 16TCh. 2 - Prob. 17TCh. 2 - 18. Life Science: decay rate. The decay rate of...Ch. 2 - Prob. 19TCh. 2 - Business: effect of advertising. Twin City...Ch. 2 - Prob. 21TCh. 2 - Prob. 22TCh. 2 - Differentiate: y=x(lnx)22xlnx+2x.Ch. 2 - Prob. 24TCh. 2 - Prob. 25TCh. 2 - Prob. 26TCh. 2 - Prob. 1ETECh. 2 - Use the exponential function to predict gross...Ch. 2 - Prob. 3ETECh. 2 - Prob. 4ETECh. 2 - Prob. 5ETECh. 2 - Prob. 7ETECh. 2 - Prob. 8ETECh. 2 - Prob. 9ETECh. 2 - Prob. 10ETECh. 2 - Prob. 11ETECh. 2 - Prob. 12ETE
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