Q&A Hero

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

Q: Use formal substitution to find the indefinite integral . A) B) C) D) E)

Q: Find the indefinite integral of the following function and check the result by differentiation. A) B) C) D) E)

Q: Find the indefinite integral of the following function and check the result by differentiation. A) B) C) D) E)

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

Q: Find the indefinite integral of the following function and check the result by differentiation. A) B) C) D) E) none of the above

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

Q: Find the indefinite integral of the following function and check the result by differentiation. A) B) C) D) E) none of the above

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

Q: Find the indefinite integral of the following function and check the result by differentiation. A) B) C) D) E) none of the above

Q: Identify u and for the integral . A) and B) and C) and D) and E) and

Q: Identifyand for the integral . A) and B) and C) and D) and E) and

Q: An evergreen nursery sells a certain shrub after 8 years. The growth rate of the shrub is given by , where t is the time in years and h is the height in centimeters. The seedlings are 14 centimeters tall when planted (t = 0). How tall are the shrubs when they are sold? A) 166 centimeters B) 172 centimeters C) 208 centimeters D) 222 centimeters E) 270 centimeters

Q: A ball is thrown vertically upwards from a height of 10 ft with an initial velocity of 40 ft per second. How high will the ball go?A) 85.0000 ftB) 28.7500 ftC) 35.0000 ftD) 65.0000 ftE) 88.6000 ft

Q: Find the cost function for the marginal cost and fixed cost of (for x = 0). A) B) C) D) E)

Q: Find a function that satisfies the conditions . A) B) C) D) E)

Q: Find the particular solution that satisfies the differential equation and initial condition . A) B) C) D) E)

Q: The graph of the derivative of a function is given below. Sketch the graphs of two functions that have the given derivative. A)B)C)D)E)

Q: Evaluate the 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 indefinite integral and check the result by differentiation. A) B) C) D) E)

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

Q: Find the indefinite integral and check the result by differentiation. A) B) C) D) E) none of the above

Q: Use algebra to rewrite the integrand; then integrate and simplify. A) B) C) D) E)

Q: Find the indefinite integral and check your result by differentiation. A) B) C) D) E)

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

Q: Find the indefinite integral and check your result by differentiation. A) B) C) 12 D) E)

Q: Estimate the surface area of the golf green shown in the figure using the midpoint rule. A) 780 B) 156 C) 1404 D) 1502 E) 524

Q: Use the Midpoint Rule with to approximate where . Then use a graphing utility to evaluate the definite integral. Compare your results. A) a. Midpoint Rule: b. Graphing utility: B) a. Midpoint Rule: b. Graphing utility: C) a. Midpoint Rule: b. Graphing utility: D) a. Midpoint Rule: b. Graphing utility: E) a. Midpoint Rule: b. Graphing utility:

Q: Estimate the surface area of the oil spill shown in the figure using the Midpoint Rule. A) 481.6B) 301.6C) 311.6D) 431.6E) 381.6

Q: Estimate the surface area of the pond shown in the figure using the Midpoint Rule. A) B) C) D) E)

Q: Use the Midpoint Rule n = 4 to approximate the area of the following region. A) 2.5B) 1.2C) 1.5D) 1.9E) 2.3

Q: Use the Midpoint Rule with to approximate the area of the region bounded by the graph of and the -axis over the interval. Sketch the region. A) The approximate area is: B) The approximate area is: C) The approximate area is: D) The approximate area is: E) The approximate area is:

Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of and the x-axis over the interval [0,1]. A) 3.7882 B) 3.3484 C) 3.5575 D) 4.3461 E) 3.3461

Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of and the x-axis over the interval []. A) 13.5671 B) 13.1273 C) 13.3364 D) 13.1250 E) 14.1250

Q: Determine the principal P that must be invested at interest rate r compounded continuously, so that $1,000,000 will be available for retirement in years , . A) $49787.07 B) $50787.07 C) $49000.04 D) $40000.06

Q: The management of a factory finds that the maximum number of units a worker can produce in a day is 30. The learning curve for the number of units N produced per day after a new employee has worked days is modeled by After 20 days on the job, a worker is producing 19 units in a day. How many days should pass before this worker is producing 25 units per day? A) about 36 days. B) about 45 days. C) about 30 days. D) about 10 days.

Q: What percent of a present amount of radioactive radium will remain after 900 years? A) 45% B) 25% C) 65% D) 68%.

Q: Use the given information to write an exponential equation for y. Does the function represent exponential growth or exponential decay? A) B) C) D)

Q: The cumulative sales (in thousands of units) of a new product after it has been on the market for t years may be modeled by . During the first year, 5000 units were sold. What is the saturation point for this product? How many units will be sold after 6 years? A) The saturation point for the market is 3000 units and 19,953 units will be sold after 6 years. B) The saturation point for the market is 30,000 units and 27,366 units will be sold after 6 years. C) The saturation point for the market is 30,000 units and 19,953 units will be sold after 6 years. D) The saturation point for the market is 30,000 units and 20,076 units will be sold after 6 years. E) The saturation point for the market is 3000 units and 27,366 units will be sold after 6 years.

Q: The effective yield is the annual rate i that will produce the same interest per year as the nominal rate compounded n times per year. For a rate that is compounded n times per year, the formula for effective yield is given as . Find the effective yield for a nominal rate of 6%, compounded monthly. Round your answer to two decimal places. A) 0.62% B) 6.41% C) 6.80% D) 1.18% E) 6.17%

Q: The number of a certain type of bacteria increases continuously at a rate proportional to the number present. There are 200 present initially, and 400 present 7 hours later. How many will there be 20 hours after the initial time? Round your answer to the nearest integer. A) 28 bacteria B) 1344 bacteria C) 1449 bacteria D) 41 bacteria E) 36 bacteria

Q: Carbon-14(14C) dating assumes that the carbon on the Earth today has the same radioactive content as it did centuries ago. If this is true, then the amount of 14C absorbed by a tree that grew several centuries ago should be the same as the amount of 14C absorbed by a similar tree today. A piece of ancient charcoal contains only 18% as much of the radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal? (The half-life of 14C is 5715 years.) Round your answer to the nearest integer. A) 2,310 years B) 33,123 years C) 2,315 years D) 14,139 years E) 14,144 years

Q: Use the given information to write an equation for y.A) B) C) D) E)

Q: Find the exponential function that passes through the two given points and . A) B) C) D) E)

Q: The cost of producing x units of a product is modeled by . Find the minimum average cost analytically. Round your answer to two decimal places. A) 200.00 dollars per unit B) 199.40 dollars per unit C) 199.18 dollars per unit D) 201.41 dollars per unit E) 199.28 dollars per unit

Q: The cost of producing x units of a product is modeled by . Find the average cost function . A) B) C) D) E)

Q: Find the y-value at the relative minima, and use a graphing utility to check your result. A) B) C) D) E) does not exist

Q: Locate any relative extrema and inflection points of the function . A) relative minimum at ; inflection point at B) relative minimum at ; no inflection points C) no relative maximum or minimum; inflection point at D) no relative extrema or inflection points. E) relative maximum at ; inflection point at

Q: Locate any relative extrema and inflection points of the function . A) no relative extrema; inflection point at B) relative maximum at ; inflection point at C) relative minimum at ; inflection point at D) no relative extrema; inflection point at E) relative minimum at ; no inflection points

Q: Locate any relative extrema and inflection points of the function . Use a graphing utility to confirm your results. A) relative maximum value at ; inflection point at x = 0 B) relative minimum value at ; inflection point at x = 0 C) relative minimum value at ; no inflection points D) relative minimum value at ; no inflection points E) relative maximum value at ; no inflection points

Q: Find the relative maxima, and use a graphing utility to check your results. A) B) C) D) E) does not exist

Q: Find the relative minima, and use a graphing utility to check your results. A) B) C) D) E) does not exist

Q: The relationship between the number of decibels and the intensity of a sound I in watts per square centimeter is given by . Find the rate of change in the number of decibels when the intensity is watt per square centimeter. Round your answer to the nearest decibel. A) 434 decibels per watt per square cm B) 43,429 decibels per watt per square cm C) 4343 decibels per watt per square cm D) 434,294 decibels per watt per square cm E) 4345 decibels per watt per square cm

Q: Find the second derivative of the function . A) B) C) D) E)

Q: Find the second derivative of the function . A) B) C) D) E)

Q: Write the equation of the line tangent to the curve A) B) C) D) E)

Q: If A) B) C) D) E)

Q: Find an equation of the tangent line to the graph of at the point . A) B) C) D) E) none of the above

Q: For , calculate to three decimal places. A) 1.609 B) "40.236 C) "13.047 D) "1.000 E) "8.047

Q: Find if . A) B) C) D) E)

Q: Find . A) B) C) D) E)

Q: Find the derivative of the following function. A) B) C) D) E)

Q: Find . A) B) C) D) E)

Q: Use a calculator to evaluate the logarithm . Round your answer to three decimal places. A) 0.197 B) 2.444 C) 6.360 D) 3.717 E) 5.087

Q: Use a change-of-base formula to rewrite the logarithm in terms of natural logarithms. A) B) C) D) E)

Q: Find . A) B) C) D) E)

Q: Find if A) B) C) D) E)

Q: Find . A) B) C) D) E)

Q: Find if A) B) C) D) E)

Q: Find . A) B) C) D) E)

Q: Find . A) B) C) D) E)

Q: Find . A) B) C) D) E)

Q: Find . A) B) C) D) E)

Q: Find . A) B) C) D) E)

Q: Find the derivative of the function . A) B) C) D) E)

Q: Find the derivative of the function . A) B) C) D) E)

Q: Find the derivative of the function . A) B) C) D) E)

Q: Find the derivative of the following function. A) B) C) D) E)