Q&A Hero

Q: Use the error formulas to find n such that the error in the approximation of the definite integral is less than 0.0001 using the Trapezoidal Rule. A) 25 B) 26 C) 24 D) 22 E) 23

Q: Use Simpson's Rule to approximate the revenue for the marginal revenue function with n = 4. Assume that the number of units sold, x, increases from 12 to 16. Round your answer to one decimal place. A) $1602.40 B) $678.36 C) $1346.14 D) $1439.03 E) $1230.54

Q: Approximate the integral using Simpson's Rule: , n = 6. Round your answer to three decimal places. A) 1.161 B) 1.284 C) 0.850 D) 0.652 E) 1.017

Q: The capitalized cost of an asset is given by where is the original investment, is the time in years, is the annual interest rate compounded continuously, and is the annual cost of maintenance (in dollars). Find the capitalized cost of an asset (a) for 5 years, (b) for 10 years, and (c) forever. A) a. For $253,901.30 b. For $807,922.43 c. For $4,466,666.67 B) a. For $453,901.30 b. For $807,922.43 c. For $1,466,666.67 C) a. For $453,901.30 b. For $2807,922.43 c. For $4,466,666.67 D) a. For $453,901.30 b. For $807,922.43 c. For $4,466,666.67 E) a. For $453,901.30 b. For $807,922.43 c. For $466,666.67

Q: Determine the amount of money required to set up a charitable endowment that pays the amount each year indefinitely for the annual interest rate compounded continuously. A) $210,000 B) $200,000 C) $220,000 D) $240,000 E) $230,000

Q: Decide whether the integral is proper or improper. A) The integral is improper.B) The integral is proper.

Q: Use the Trapezoidal Rule to approximate the value of the definite integral . Round your answer to three decimal places. A) 6.7643 B) 2.7931 C) 2.7955 D) 4.6552 E) 4.6615

Q: Approximate the definite integral "by hand," using the Trapezoidal Rule with trapezoids. Round answer to three decimal places. A) 11.425 B) 11.381 C) 5.691 D) 8.569 E) 15.175

Q: The revenue (in dollars per year) for a new product is modeled by where t the time in years. Estimate the total revenue from sales of the product over its first 3 years on the market. Round your answer to nearest dollar A) $6579 B) $3291 C) $10,821 D) $15,830 E) $1138

Q: Use the table of integrals to find the average value of the growth function over the interval , where N the size of a population and t is the time in days. Round your answer to three decimal places. A) 248.346 B) 1057.983 C) 246.346 D) 680.477 E) 682.451

Q: The probability of recall in an experiment is modeled by where x is the percent of recall. What is the probability of recalling between 60% and 90%? Round your answer to three decimal places. A) 0.432 B) 0.270 C) 0.710 D) 0.219 E) 0.936

Q: Evaluate the definite integral dx. Round your answer to three decimal places. A) 6.144 B) 7.207 C) 4.541 D) 5.644 E) 4.881

Q: Evaluate the definite integral . Round your answer to three decimal places. A) 20.210 B) 16.873 C) 32.580 D) 26.395 E) 4.504

Q: A body assimilates a 12-hour cold tablet at a rate modeled by where is measured in milligrams per hour and is the time in hours. Use Simpson's Rule with to estimate the total amount of the drug absorbed into the body during the 12 hours. A) 58.915 mg B) 68.915 mg C) 38.915 mg D) 48.915 mg E) 78.915 mg

Q: The rate of change in the number of subscribers to a newly introduced magazine is modeled by where is the time in years. Use Simpson's Rule with to estimate the total increase in the number of subscribers during the first 6 years. A) 1870 subscribers B) 1780 subscribers C) 1800 subscribers D) 1878 subscribers E) 1987 subscribers

Q: Approximate the value of the definite integral using (a) the Trapezoidal Rule and (b) Simpson's Rule for the indicated value of n. Round your answers to three significant digits. A) a. Trapezoidal Rule: b. Simpson's Rule: B) a. Trapezoidal Rule: b. Simpson's Rule: C) a. Trapezoidal Rule: b. Simpson's Rule: D) a. Trapezoidal Rule: b. Simpson's Rule: E) a. Trapezoidal Rule: b. Simpson's Rule:

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the indicated value of n. Compare these results with the exact value of the definite integral. Round your answers to four decimal places. A) a. Exact: b. Trapezoidal Rule: c. Simpson's Rule: B) a. Exact: b. Trapezoidal Rule: c. Simpson's Rule: C) a. Exact: b. Trapezoidal Rule: c. Simpson's Rule: D) a. Exact: b. Trapezoidal Rule: c. Simpson's Rule: E) a. Exact: b. Trapezoidal Rule: c. Simpson's Rule:

Q: Use a table of integrals to find the indefinite integral . A) B) C) D) E)

Q: Use a table of integrals to find the indefinite integral . A) B) C) D) E)

Q: Use a table of integrals with forms involving to find A) B) C) D) E)

Q: Use a table of integrals to find the indefinite integral . A) B) C) D) E)

Q: Use a table of integrals with forms involving a + bu to find A) B) C) D) E)

Q: Find the integral below using an integral table. A) B) C) D) E)

Q: Use a table of integrals with forms involving to find the integral. A) B) C) D) E)

Q: Use a table of integrals to find the indefinite integral . A) B) C) D) E)

Q: Present Value of a Continuous Stream of Income. An electronics company generates a continuous stream of income of million dollars per year, where t is the number of years that the company has been in operation. Find the present value of this stream of income over the first 9 years at a continuous interest rate of 12%. Round answer to one decimal place. A) $143.7 million B) $81.6 million C) $182.7 million D) $343.2 million E) $85.8 million

Q: A model for the ability M of a child to memorize, measured on a scale from 0 to 10, is where t is the child's age in years. Find the average value predicted by the model for a child's ability to memorize between first and second birthdays. Round your answer to three decimal places. A) 3.318 B) 2.218 C) 4.118 D) 1.318 E) 2.018

Q: Use integration by parts to find the integral below. A) B) C) D) E)

Q: Find the definite integral. A) B) C) D) E) none of the above

Q: Evaluate the definite integral . Round your answer to three decimal places. A) 828.111 B) 207.823 C) 118.290 D) 207.811 E) 79.245

Q: Find the indefinite integral. A) B) C) D) E) none of the above

Q: Find the indefinite integral. A) B) C) D) E)

Q: Find the indefinite integral. A) B) C) D) E)

Q: Find the indefinite integral. A) B) C) D) E)

Q: Use integration by parts to evaluate . A) B) C) D) E)

Q: Find the indefinite integral. A) B) C) D) E)

Q: Use integration by parts to find the integral below. A) B) C) D) E)

Q: Use integration by parts to evaluate. Note that evaluation may require integration by parts more than once. A) B) C) D) E)

Q: Find the indefinite integral. A) B) C) D) E)

Q: Use integration by parts to evaluate A) B) C) D) E)

Q: Identify u and dv for finding the integral using integration by parts. dx A) dx; dx B) C) D) E)

Q: Identify u and dv for finding the integral using integration by parts. A) B) C) D) E)

Q: Use the rectangles to approximate the area of the region. Compare your result with the exact area obtained with a definite integral. A) a. The approximate area: 3 b. The exact area: 2 B) a. The approximate area: 2 b. The exact area: 3 C) a. The approximate area: 2 b. The exact area: 1 D) a. The approximate area: 2 b. The exact area: 2 E) a. The approximate area: 1 b. The exact area: 2

Q: Use the Midpoint Rule with n = 4 to approximate the area of the following region. A) 3B) 8C) 2D) 1E) 6

Q: The revenue from a manufacturing process (in millions of dollars per year) is projected to follow the model for 10 years. Over the same period of time, the cost (in millions of dollars per year) is projected to follow the model , where t is the time (in years). Approximate the profit over the 10-year period, beginning with t = 0. Round your answer to two decimal places. A) million B) million C) million D) million E) million

Q: Two models, and , are given for revenue (in billions of dollars per year) for a large corporation. Both models are estimates of revenues for 2007 through 2011, with t = 7 corresponding to 2007. Which model is projecting the greater revenue? How much more total revenue does that model project over the five-year period? A) The model projects greater revenue than . billion B) The model projects greater revenue than . billion C) The model projects greater revenue than . billion D) The model projects greater revenue than . billion E) The model projects greater revenue than . billion

Q: The demand function for a product is , where p is the number of dollars and x is the number of units. If the equilibrium price is , what is the consumer's surplus? A) $ B) $ C) $ D) $ E) $

Q: Find the consumer and producer surpluses by using the demand and supply functions, where p is the price (in dollars) and x is the number of units (in millions). Demand Function Supply Function A) a. $2587.50 b. $3725.00 B) a. $5587.50 b. $4725.00 C) a. $2587.50 b. $1725.00 D) a. $1587.50 b. $4725.00 E) a. $3587.50 b. $4725.00

Q: Find the area of the region bounded by the graphs of the algebraic functions. A) B) C) D) E)

Q: Find the area of the region bounded by the graphs of the algebraic functions. A) B) C) D) E)

Q: The integrand of the following definite integral is a difference of two functions. Sketch the graph of the two functions and shade the region whose area is represented by the integral.A)B)C)D)E)

Q: Set up the definite integral that gives the area of the region bounded by the graphs. A) B) C) D) E)

Q: Find the area of the shaded region. A) B) C) D) E)

Q: Determine the graph whose area (the shaded region) is represented by the integral. A)B)C)D)E)

Q: The rate of depreciation of a building is given by dollars per year,Use the definite integral to find the total depreciation over the first years. A) B) C) D) E)

Q: Find the average value of the function over the given interval. on [0,1] A) B) C) D) E)

Q: Find the average value of the function over the given interval. on [-3,3] A) 15 B) 52.5 C) 90 D) 10 E) 50

Q: Find the area between the curve and the x-axis from . A) B) C) D) E)

Q: Evaluate the following definite integral. Use a graphing utility to check your answer. A) B) C) D) E)

Q: Evaluate the definite integral of the algebraic function.Use a graphing utility to verify your results.A) -67.0832B) -115.0555C) 101.7168D) 17.3168E) -182.1386

Q: Evaluate the definite integral . A) B) C) D) E)

Q: Evaluate the definite integral of the algebraic function.Use a graphing utility to verify your results.A) -6B) -6C) 13D) 18E) -3

Q: Determine the area of the given region. A) B) C) D) E) None of the above

Q: Use the valuesandto evaluate the definite integral.A) 21B) -9C) 1D) 11E) -7

Q: Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral. A) B) C) D) E) none of the above

Q: Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.A) -318B) 636C) 336D) 168E) 12

Q: Find the equation of the function whose derivative is and whose graph passes through the point . A) B) C) D) E)

Q: Use any basic integration formula or formulas to find the indefinite integral . A) B) C) D) E)

Q: Find the indefinite integral. A) B) C) D) E) none of the above

Q: Find the indefinite integral. A) B) C) D) E)

Q: Find the indefinite integral. A) B) C) D) integral does not exist E) none of the above

Q: Find the indefinite integral. A) B) C) D) E)

Q: Find the indefinite integral. A) B) C) D) E)

Q: Use the Log Rule to find the indefinite integral for . A) B) C) D) E)

Q: Evaluate the integral A) B) C) D) E)

Q: Find the indefinite integral. A) B) C) D) E)

Q: Evaluate the integral A) B) C) D) E)

Q: Evaluate the integral A) B) C) D) E)

Q: Find the supply function that satisfies and the initial condition x = 600 when . A) B) C) D) E)

Q: The marginal cost of a product is modeled by , when x = 3, C = 90. Find the cost function. A) B) C) D) E)