DPT Diagnostic Prerequisite Test 1 Functions And Graphs 2 Limits And The Derivative 3 Additional Derivative Topics 4 Graphing And Optimization 5 Integration 6 Additional Integration Topics 7 Multivariable Calculus 8 Trigonometric Functions 9 Differential Equations 10 Taylor Polynomial And Infinite Series 11 Probability And Calculus A.1 Real Numbers A.2 Operations On Polynomials A.3 Factoring Polynomials A.4 Operations On Rational Expressions A.5 Integer Exponents And Scientific Notation A.6 Rational Exponents And Radicals A.7 Quadratic Equations B.1 Sequences, Series, And Summation Notation B.2 Arithmetic And Geometric Sequences B.3 Binomial Theorem B.4 Interpolating Polynomials And Divided Differences expand_more
5.1 Antiderivatives And Indefinite Integrals 5.2 Integration By Substitution 5.3 Differential Equations; Growth And Decay 5.4 The Definite Integral 5.5 The Fundamental Theorem Of Calculus Chapter Questions expand_more
Problem 1MP: Matched Problem 1 Repeat Example 1 for the daily cost function C(x) = 7.5x2 + 305x + 625 EXAMPLE 1... Problem 2MP: Matched Problem 2 Evaluated 13(4x2ex+5x)dx. Problem 3MP: Matched Problem 3 Use both methods described in Example 3 to evaluate 0112x+4dx. Problem 4MP: Matched Problem 4 Use both method 2 described in Example 3 to evaluate 2516tdt. Problem 5MP: Matched Problem 5 Repeat Example 5 if P(x)=3000.2x0x3,000 and monthly production is increased from... Problem 6MP: Matched Problem 6 Repeat Example 6 if C(t) = 1 and R(t)=7.5e0.5t. EXAMPLE 6 Useful Life An amusement... Problem 7MP: c 1.54.3xlnxdx to three decimal places. Problem 8MP: Matched Problem 8 Find the average value of g(t) = 6t2 2t over the interval [2, 3]. Problem 9MP: Matched Problem 9 Given the supply equation p=S(x)=10e0.05x find the average price (in dollars) over... Problem 1ED Problem 1E: In Problems 18, use geometric formulas to find the unsigned area between the graph of y = f(x) and... Problem 2E: In Problems 18, use geometric formulas to find the unsigned area between the graph of y = f(x) and... Problem 3E: In Problems 18, use geometric formulas to find the unsigned area between the graph of y = f(x) and... Problem 4E: In Problems 18, use geometric formulas to find the unsigned area between the graph of y = f(x) and... Problem 5E: In Problems 18, use geometric formulas to find the unsigned area between the graph of y = f(x) and... Problem 6E: In Problems 18, use geometric formulas to find the unsigned area between the graph of y = f(x) and... Problem 7E: In Problems 18, use geometric formulas to find the unsigned area between the graph of y = f(x) and... Problem 8E: In Problems 18, use geometric formulas to find the unsigned area between the graph of y = f(x) and... Problem 9E: A In Problems 912, (A) Calculate the change in F(x) from x = 10 to x = 15. (B) Graph F(x) and use... Problem 10E: A In Problems 912, (A) Calculate the change in F(x) from x = 10 to x = 15. (B) Graph F(x) and use... Problem 11E Problem 12E: A In Problems 912, (A) Calculate the change in F(x) from x = 10 to x = 15. (B) Graph F(x) and use... Problem 13E: Evaluate the integrals in Problems 1332. 13. 057dx Problem 14E: Evaluate the integrals in Problems 1332. 14. 042xdx Problem 15E: Evaluate the integrals in Problems 1332. 15. 024xdx Problem 16E: Evaluate the integrals in Problems 1332. 16. 035dx Problem 17E: Evaluate the integrals in Problems 1332. 17. 25x2dx Problem 18E Problem 19E: Evaluate the integrals in Problems 1332. 19. 131xdx Problem 20E: Evaluate the integrals in Problems 1332. 20. 131x2dx Problem 21E: Evaluate the integrals in Problems 1332. 21. 231x2dx Problem 22E Problem 23E: Evaluate the integrals in Problems 1332. 23. 032exdx Problem 24E: Evaluate the integrals in Problems 1332. 24. 023exdx Problem 25E: Evaluate the integrals in Problems 1332. 25. 57(3x+2)dx Problem 26E Problem 27E: Evaluate the integrals in Problems 1332. 27. 75(3x+2)dx Problem 28E: Evaluate the integrals in Problems 1332. 28. 51(2x1)dx Problem 29E: Evaluate the integrals in Problems 1332. 29. 23(4x36x2+10x)dx Problem 30E: Evaluate the integrals in Problems 1332. 30. 14(5x412)dx Problem 31E: Evaluate the integrals in Problems 1332. 31. 33(4x36x2+10x)8dx Problem 32E: Evaluate the integrals in Problems 1332. 32. 44(5x412)9dx Problem 33E: B Evaluate the integrals in Problems 3348. 33. 12(2x23)dx Problem 34E: B Evaluate the integrals in Problems 3348. 34. 12(516x3)dx Problem 35E: B Evaluate the integrals in Problems 3348. 35. 143xdx Problem 36E: B Evaluate the integrals in Problems 3348. 36. 4252xdx Problem 37E: B Evaluate the integrals in Problems 3348. 37. 2312(x24)5xdx Problem 38E: B Evaluate the integrals in Problems 3348. 38. 0132(x2+1)7xdx Problem 39E: B Evaluate the integrals in Problems 3348. 39. 391x1dx Problem 40E: B Evaluate the integrals in Problems 3348. 40. 281x+1dx Problem 41E: B Evaluate the integrals in Problems 3348. 41. 510e0.05xdx Problem 42E: B Evaluate the integrals in Problems 3348. 42. 1025e0.01xdx Problem 43E: B Evaluate the integrals in Problems 3348. 43. 1elnttdt Problem 44E: B Evaluate the integrals in Problems 3348. 44. ee2(lnt)2tdt Problem 45E: B Evaluate the integrals in Problems 3348. 45. 01xex2dx Problem 46E: B Evaluate the integrals in Problems 3348. 46. 01xex2dx Problem 47E: B Evaluate the integrals in Problems 3348. 47. 11ex2dx Problem 48E Problem 49E: In Problems 4956, (A)Find the average value of each function over the indicated interval. (B)Use a... Problem 50E Problem 51E: In Problems 4956, (A)Find the average value of each function over the indicated interval. (B)Use a... Problem 52E: In Problems 4956, (A)Find the average value of each function over the indicated interval. (B)Use a... Problem 53E: In Problems 4956, (A)Find the average value of each function over the indicated interval. (B)Use a... Problem 54E Problem 55E: In Problems 4956, (A)Find the average value of each function over the indicated interval. (B)Use a... Problem 56E: In Problems 4956, (A)Find the average value of each function over the indicated interval. (B)Use a... Problem 57E: C Evaluate the integrals in Problems 5762. 57. 23x2x23dx Problem 58E: C Evaluate the integrals in Problems 5762. 58. 01x3x2+2dx Problem 59E: C Evaluate the integrals in Problems 5762. 59. 01x1x22x+3dx Problem 60E: C Evaluate the integrals in Problems 5762. 60. 12x+12x2+4x+4dx Problem 61E: C Evaluate the integrals in Problems 5762. 61. 11exex(ex+ex)2dx Problem 62E: C Evaluate the integrals in Problems 5762. 62. 67ln(t5)t5dt Problem 63E Problem 64E: Use a numerical integration routine to evaluate each definite integral in Problems 6366 (to three... Problem 65E: Use a numerical integration routine to evaluate each definite integral in Problems 6366 (to three... Problem 66E: Use a numerical integration routine to evaluate each definite integral in Problems 6366 (to three... Problem 67E: The mean value theorem states that if F(x) is a differentiable function on the interval [a, b], then... Problem 68E Problem 69E: Cost. A company manufactures mountain bikes. The research department produced the marginal cost... Problem 70E: Cost. Referring to Problem 69, compute the increase in cost going from a production level of 0 bikes... Problem 71E: Salvage value. A new piece of industrial equipment will depreciate in value, rapidly at first and... Problem 72E: Maintenance costs. Maintenance costs for an apartment house generally increase as the building gets... Problem 73E: 73. Employee training. A company producing computer components has established that, on the average,... Problem 74E Problem 75E: Useful life. The total accumulated costs C(t) and revenues R(t) (in thousands of dollars),... Problem 76E: Useful life. The total accumulated costs C(t) and revenues R(t) (in thousands of dollars),... Problem 77E: Average cost. The total cost (in dollars) of manufacturing x auto body frames is C(x) = 60,000 +... Problem 78E: Average cost. The total cost (in dollars) of printing x dictionaries is C(x) = 20,000 + 10x. (A)... Problem 79E: Sales. The rate at which the total number of sales is changing is given by S(t) where t is the... Problem 80E Problem 81E: Supply function. Given the supply function p=S(x)=10(e0.02x1) find the average price (in dollars)... Problem 82E: Demand function. Given the demand function p=D(x)=1,000x find the average price (in dollars) over... Problem 83E: Labor costs and learning. A defense contractor is starting production on a new missile control... Problem 84E: Labor costs and learning. If the rate of labor use in Problem 83 is L(x)=2,000x1/3 then... Problem 85E Problem 86E: Repeat Problem 85 with an order of 1.200 units every 4 months. What is the average number of units... Problem 87E: Oil production. Using production and geological data, the management of an oil company estimates... Problem 88E Problem 89E: Biology. A yeast culture weighing 2 grams is expected to grow at the rate of W(t) = 0.2e0.1t grams... Problem 90E: Medicine. The rate at which the area of a skin wound is increasing is given (in square centimeters... Problem 91E: Temperature. If the temperature in an aquarium (in degrees Celsius) is given by C(t)=t32t+100t2 over... Problem 92E: Medicine. A drug is injected into the bloodstream of a patient through her right arm. The drug... Problem 93E: Politics. Public awareness of a congressional candidate before and after a successful campaign was... Problem 94E: Population composition. The number of children in a large city was found to increase and then... format_list_bulleted