Problem 1CQ: What is an antiderivative? Give an example. Problem 2CQ Problem 3CQ Problem 4CQ Problem 1E: In Exercises 1-4, verify directly that F is an antiderivative of f. 1. F(x)=13x3+2x2x+2;f(x)=x2+4x1 Problem 2E: In Exercises 1-4, verify directly that F is an antiderivative of f. 2. F(x) = xex + ; f(x) = ex(1 +... Problem 3E: In Exercises 1-4, verify directly that F is an antiderivative of f. 3. F(x)=2x21;f(x)=2x2x21 Problem 4E Problem 5E Problem 6E: In Exercises 5-8, (a) verify that G is an antiderivative of f, (b) find all antiderivatives of f,... Problem 7E: In Exercises 5-8, (a) verify that G is an antiderivative of f, (b) find all antiderivatives of f,... Problem 8E Problem 9E: In Exercises 9-50, find the indefinite integral 9. 6dx Problem 10E: In Exercises 9-50, find the indefinite integral 10. 2dx Problem 11E: In Exercises 9-50, find the indefinite integral 11. x3dx Problem 12E: In Exercises 9-50, find the indefinite integral 12. 2x5dx Problem 13E: In Exercises 9-50, find the indefinite integral 13. x4dx Problem 14E: In Exercises 9-50, find the indefinite integral 14. 3t7dt Problem 15E: In Exercises 9-50, find the indefinite integral 15. x2/3dx Problem 16E: In Exercises 9-50, find the indefinite integral 16. 2u3/4du Problem 17E: In Exercises 9-50, find the indefinite integral 17. x5/4dx Problem 18E: In Exercises 9-50, find the indefinite integral 18. 3x2/3dx Problem 19E: In Exercises 9-50, find the indefinite integral 19. 2x3dx Problem 20E: In Exercises 9-50, find the indefinite integral 20. 13x5dx Problem 21E: In Exercises 9-50, find the indefinite integral 21. tdx Problem 22E: In Exercises 9-50, find the indefinite integral 22. 3tdx Problem 23E: In Exercises 9-50, find the indefinite integral 23. (34x)dx Problem 24E: In Exercises 9-50, find the indefinite integral 24. (1+u+u2)dx Problem 25E Problem 26E: In Exercises 9-50, find the indefinite integral 26. (0.3t2+0.02t+2)dt Problem 27E Problem 28E Problem 29E: In Exercises 9-50, find the indefinite integral 29. (1+x+ex)dx Problem 30E: In Exercises 9-50, find the indefinite integral 30. (2+x+2x2+ex)dx Problem 31E: In Exercises 9-50, find the indefinite integral 31. (4x32x21)dx Problem 32E Problem 33E Problem 34E Problem 35E Problem 36E Problem 37E: In Exercises 9-50, find the indefinite integral 37. (u3+2u2u3u)du Hint: u3+2u2u3u=13u2+23u13 Problem 38E Problem 39E Problem 40E: In Exercises 9-50, find the indefinite integral 40. u2(1u2+u4)du Problem 41E: In Exercises 9-50, find the indefinite integral 41. 1x2(x42x2+1)dx Problem 42E Problem 43E: In Exercises 950, find the indefinite integral 43. ds(s+1)2 Problem 44E: In Exercises 950, find the indefinite integral 44. (x+3x2ex)dx Problem 45E: In Exercises 950, find the indefinite integral 45. (et+te)dx Problem 46E Problem 47E: In Exercises 950, find the indefinite integral 47. x3+x2x+1x2dx Hint: Simplify the integrand first Problem 48E: In Exercises 950, find the indefinite integral 48. t3+t3t2dt Hint: Simplify the integrand first Problem 49E: In Exercises 950, find the indefinite integral 49. (x1)2x2dx Hint: Simplify the integrand first Problem 50E: In Exercises 950, find the indefinite integral 50. (x+1)2(11x)dx Hint: Simplify the integrand first Problem 51E Problem 52E: In Exercises 5158, find f(x) by solving the initial-value problem. 51. f(x) = 3x2 6; f(2) = 4 Problem 53E Problem 54E: In Exercises 5158, find f(x) by solving the initial-value problem. 54. f(x)=1x;f(4)=2 Problem 55E: In Exercises 5158, find f(x) by solving the initial-value problem. 55. f(x)=1+1x2;f(1)=3 Problem 56E: In Exercises 5158, find f(x) by solving the initial-value problem. 56. f(x) = ex 2x; f(0) = 2 Problem 57E: In Exercises 5158, find f(x) by solving the initial-value problem. 57. f(x)=x+1x;f(1)=1 Problem 58E: In Exercises 5158, find f(x) by solving the initial-value problem. 58. f(x)=1+ex+1x;f(1)=3+e Problem 59E Problem 60E: In Exercises 5962, find the function f given that the slope of the tangent line to the graph of f at... Problem 61E Problem 62E: In Exercises 5962, find the function f given that the slope of the tangent line to the graph of f at... Problem 63E Problem 64E: VELOCITY OF A CAR Two cars, side by side, start from rest and travel along a straight road. The... Problem 65E Problem 66E: Households Owning More Than One TV Television is the most popular mass medium in the United States.... Problem 67E: VELOCITY of a Maglev The velocity (ill feet per second) at time t of a maglev is v(t) = 0.2t + 3 (0 ... Problem 68E: REVENUE Functions The management of Lorimar Watch Company has determined that the daily marginal... Problem 69E: Profit FUNCTIONS Camion Precision Instruments makes an automatic electronic flash with Thyrister... Problem 70E: Cost of Producing Guitars Carlota Music Company estimates that the marginal cost of manufacturing... Problem 71E: Wind Energy in China Chinas push to install more wind energy capacity has started paying off. As of... Problem 72E: Growth of National Health Costs National health expenditures are projected to grow at the rate of... Problem 73E: Genetically Modified Crops The total number of acres of genetically modified crops grown in... Problem 74E: Velocity of a Car The velocity of a car (in feet per second) t sec after starting from rest is given... Problem 75E: Ballast Dropped from a Balloon A ballast is dropped from a stationary hot-air balloon that is... Problem 76E: POPULATION GROWTH The development of Astro World (The Amusement Park of the Future) on the outskirts... Problem 77E: CABLE TV Subscribers A study conducted by TeleCable estimates that the number of cable TV... Problem 78E Problem 79E Problem 80E: QUALITY Control As part of a quality-control program, the chess sets manufactured by Jones Brothers... Problem 81E Problem 82E: RISK of DOWN SYNDROME The rate at which the risk of Down syndrome is changing is approximated by the... Problem 83E: AMOUNT of RAINFALL During a thunderstorm, rain was falling at the rate of 82t32t3 (0 t 0.6)... Problem 84E: SALARIES of MARRIED WOMEN The percentage of married women who earned more than their husbands over... Problem 85E: SOCIAL Networks The percentage of people age 12 years and older using social network sites and/or... Problem 87E: SURFACE Area OF A Human Empirical data suggest that the surface area of a 180-cm-tall human body... Problem 88E: OZONE pollution The rate of change of the level of ozone, an invisible gas that is an irritant and... Problem 89E: HEIGHTS of Children According to the Jenss model for predicting the height of preschool children,... Problem 90E: ACCELERATION OF a car A car traveling along a straight road at 66 ft/sec accelerated to a speed of... Problem 91E Problem 92E: CARRIER Landing A pilot lands a fighter aircraft on an aircraft carrier. At the moment of touchdown,... Problem 93E: CROSSING the Finish Line After rounding the final turn in the bell lap, two runners emerge ahead of... Problem 94E: DRAINING a tank A tank has a constant cross-sectional area of 50 ft2 and an orifice of constant... Problem 95E: LAUNCHING A FIGHTER AIRCRAFT A fighter aircraft is launched from the deck of a Nimitz-class aircraft... Problem 96E Problem 97E Problem 98E Problem 99E Problem 100E: In Exercises 96-100, determine whether the statement is true or false. If it is true, explain why it... format_list_bulleted