Q&A Hero

Q: Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If A) TrueB) False. The product rule is

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

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

Q: Find the second derivative of the function. A) B) C) D) E) None of the above

Q: The value V of a machineyears after it is purchased is inversely proportional to the square root of . The initial value of the machine is10,000. Find the rate of depreciation when . Round your answer to two decimal places.A) -603.68 per yearB) -1889.82 per yearC) 1767.77 per yearD) 447.21 per yearE) -1207.36 per year

Q: You deposit 4000 in an account with an annual interest rate of change r (in decimal form) compounded monthly. At the end of 4 years, the balance is . Find the rates of change of A with respect to r when . A) 6709.32 B) 318,595.99 C) 559.11 D) 26549.67 E) 26,265.13

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 given function. Simplify and express the answer using positive exponents only. A) B) C) D) E)

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

Q: Differentiate the given function. A) B) C) D) E)

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

Q: Find of ,. A) B) C) D) E) none of these choices

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

Q: A population of bacteria is introduced into a culture. The number of bacteria P can be modeled by where t is the time (in hours). Find the rate of change of the population when . A) 31.03 units per dollar B) 1.75 units per dollar C) 7.01 units per dollar D) 3.63 units per dollar E) 7.76 units per dollar

Q: Use the demand function to find the rate of change in the demand x for the given price . Round your answer to two decimal places.A) 26.53 units per dollarB) -6.63 units per dollarC) 6.63 units per dollarD) 36.11 units per dollarE) -26.53 units per dollar

Q: Find an equation of the tangent line to the graph of f at the given point. at A) B) C) D) E)

Q: Find an equation of the tangent line to the graph of f at the given point. at A) B) C) D) E)

Q: Use the given information to find of the function . A) B) C) D) E)

Q: A population of bacteria is introduced into a culture. The number of bacteria P can be modeled by where t is the time (in hours). Find the rate of change of the population when t = 2. A) B) C) D) E)

Q: Find the point(s), if any, at which the graph of f has a horizontal tangent line. A) B) C) D) E)

Q: Find the derivative of the function . State which differentiation rule(s) you used to find the derivative. A) 1, Product Rule. B) 1, Quotient Rule C) 5, Product Rule. D) 5, Quotient Rule E) x+3, Product Rule.

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

Q: Use the product Rule to find the derivative of the function . A) B) C) D) E)

Q: When the price of a glass of lemonade at a lemonade stand was $1.75, 400 glasses were sold. When the price was lowered to $1.50, 500 glasses were sold. Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25, respectively. Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold. A) B) C) D) E)

Q: When the price of a glass of lemonade at a lemonade stand was $1.75, 400 glasses were sold. When the price was lowered to $1.50, 500 glasses were sold. Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25, respectively. Find the profit P as a function of x, the number of glasses of lemonade sold. A) B) C) D) E)

Q: The population P ( in thousands) of Japan from 1980 through 2010 can be modeled by where t is the year, with t =0 corresponding to 1980. Determine the population growth rate, . A) B) C) D) E)

Q: The profit (in dollars) from selling x units of calculus textbooks is given by . Find the marginal profit when . Round your answer to two decimal places. A) $34.80 B) $864.80 C) $5.20 D) $20.00 E) $859.55

Q: The profit (in dollars) from selling x units of calculus textbooks is given by . Find the additional profit when the sales increase from 145 to 146 units. Round your answer to two decimal places. A) $5.45 B) $20.00 C) $5.55 D) $11.00 E) $10.80

Q: The cost C (in dollars) of producing x units of a product is given by . Find the additional cost when the production increases from 9 t o10. A) B) C) D) E)

Q: Find the marginal profit for producing x units. (The profit is measured in dollars.) A) B) C) D) E)

Q: Find the marginal revenue for producing x units. (The revenue is measured in dollars.) A) B) C) D) E)

Q: Find the marginal cost for producing x units. (The cost is measured in dollars.) A) B) C) D) E)

Q: The graph shows the number of visitors V to a national park in hundreds of thousands during a one-year period, where t = 1 represents January. Estimate the rate of change of V over the interval . Round your answer to the nearest hundred thousand visitors per year. A) 176.92 hundred thousand visitors per year B) 328.57 hundred thousand visitors per year C) 166.67 hundred thousand visitors per year D) 383.33 hundred thousand visitors per year E) 766.67 hundred thousand visitors per year

Q: Determine the point(s), (if any), at which the graph of the function has a horizontal tangent. A) B) and C) and D) E) There are no points at which the graph has a horizontal tangent.

Q: Differentiate the given function. A) B) C) D) E)

Q: Differentiate the given function. A) B) C) D) E)

Q: Find the derivative of the function. A) B) C) D) E) none of the above

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: For the function given, find A) B) C) D) E)

Q: Find the derivative of the function. A) B) C) D) E) none of the above

Q: Find the derivative of the function. A) B) C) D) E) none of the above

Q: Identify a function that has the given characteristics and then sketch the function. A) B) C) D) E)

Q: Find an equation of the a line that is tangent to the graph of f and parallel to the given line. A) B) C) D) E) both B and D

Q: Find an equation of the line that is tangent to the graph of f and parallel to the given line. A) B) C) D) E) none of the above

Q: Find the derivative of the following function using the limiting process. A) B) C) D) E) none of the above

Q: Find the derivative of the following function using the limiting process. A) B) C) D) E) either B or D

Q: Find the derivative of the following function using the limiting process. A) B) C) D) E) none of the above

Q: Use the limit definition to find the slope of the tangent line to the graph of at the point . A) B) C) D) E)

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

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

Q: Find the slope of the tangent line to the graph of the function below at the given point. A) B) C) D) E) none of the above

Q: A deposit of $7500 is made in an account that pays 6% compounded every 5 months. The amountin the account after years is , t. What are the points of discontinuity of graph of ? (Here, the brackets indicate the greatest integer function.)A) B) C) D) E)

Q: Find constants a and b such that the functionis continuous on the entire real line.A) a = 3 , b = 0B) a = 3 , b = -3C) a = 3 , b = 3D) a = -3 , b = 3E) a = -3 , b = -3

Q: Describe the interval(s) on which the function is continuous. A) and B) and C) and D) E) none of these choices

Q: Sketch the graph of the function and describe the interval(s) on which the function is continuous.A) and B) and C) and D) and E) none of these choices

Q: Find the x-values (if any) at which the function is not continuous. Which of the discontinuities are removable? A) no points of discontinuity B) (not removable), (removable) C) (removable), (not removable) D) no points of continuity E) (not removable), (not removable)

Q: Find the x-values (if any) at which the function is not continuous. Which of the discontinuities are removable? A) 2 and -2, not removable B) continuous everywhere C) 2 and -2, removable D) discontinuous everywhere E) none of the above

Q: Find the x-values (if any) at which f(x) is not continuous and identify whether they are removable or nonremovable. A) x = 1 is a removable discontinuity B) x = 1 is a nonremovable discontinuity C) x = -1 is a removable discontinuity D) x = -1 is a nonremovable discontinuity E) f(x) has no discontinuities

Q: Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing the function with a graphing utility, if one is available. A) discontinuous at B) discontinuous at C) discontinuous at D) discontinuous at E) continuous everywhere

Q: Describe the intervalson which the function is continuous. A) B) C) D) E)

Q: Find the x-values (if any) at which the function is not continuous. Which of the discontinuities are removable? A) continuous everywhere B) , removable C) , removable D) , not removable E) both B and C

Q: Determine whether the given function is continuous. If it is not, identify where it is discontinuous. A) discontinuous at B) discontinuous at C) discontinuous at D) discontinuous at E) continuous everywhere

Q: Consider a certificate of deposit that pays 14% (annual percentage rate) on an initial deposit of $4000. The balance after 14 years is . Estimate , whereis the length of the compounding period (in years). Round your answer to the nearest hundredth. A) 28,397.31 B) 1471.52 C) 4000.00 D) 56,000.00 E) 4560.00

Q: The cost (in dollars) of removing of the pollutants from the water in a small lake is given by . Evaluate . A) B) C) D) E)

Q: Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically. A) B) C) D) 0 E) does not exist

Q: Determine the following limit. (Hint: Use the graph of the function.)A) 0B) does not existC) 1D) -1E) -2

Q: Find .A) 3B) infC) 0D) -3E)

Q: Find the limit: .A) B) C) 0D) -1E) 1

Q: Find .A) 4B) 0C) D) -4E) inf

Q: Find the limit (if it exists): A) B) C) 0 D) E)

Q: Use the graph of and the given c-value to find . A) B) -5C) -7D) 3E) does not exist

Q: A graph of is shown and a c-value is given. For this problem, use the graph to find . A) 0B) 2C) -6D) -4E) does not exist

Q: Let . Determine the following limit. (Hint: Use the graph of the function.) A) 5 B) 1 C) 4 D) 16 E) does not exist.

Q: Suppose that and . Find the following limit: A) -12B) -23C) -1D) 132E) 11

Q: Suppose that and . Find the following limit: A) -88B) 19C) 0D) -3E) -11

Q: Complete the table and use the result to estimate the limit. x f(x)A) 0.121736B) 0.101736C) -0.138264D) -0.008264E) -0.118264

Q: Complete the table and use the result to estimate the limit. x f(x)A) 2.12132B) -1.99632C) -2.12132D) 1.954654E) 1.87132