[SOLVED] use derivatives to determine whether f is

> The total cost (in dollars) of printing x dictionaries is C(x) = 20,000 + 10x. (A) Find the average cost per unit if 1,000 dictionaries are produced. (B) Find the average value of the cost function over the interval [0, 1,000]. (C) Discuss the differe

> The total accumulated costs C1t2 and revenues R1t2 (in thousands of dollars), respectively, for a coal mine satisfy C′(t) = 3 and R′(t) = 15e-0.1t where t is the number of years that the mine has been in operation. Find the useful life of the mine, to

> Refer to Problem 73. (A) Find a cubic regression equation for the data, and graph it and the data set in the same viewing window. (B) Use the regression equation and a numerical integration routine on a graphing calculator to approximate the number of

> Maintenance costs for an apartment house generally increase as the building gets older. From past records, the rate of increase in maintenance costs (in dollars per year) for a particular apartment complex is given approximately by where x is the age of

> Referring to Problem 69, compute the increase in cost going from a production level of 0 bikes per month to 600 bikes per month. Set up a definite integral and evaluate it. Data from Problem 69: A company manufactures mountain bikes. The research depart

> The fundamental theorem of calculus can be proved by showing that, for every positive integer n, there is a Riemann sum for f on [a, b] that is equal to F(b) â F(a). By the mean value theorem within each subinterval [xk - 1, xk] that be

> Use a numerical integration routine to evaluate each definite integral

> Evaluate the integrals.

> Verify the results in Problem 54 by computing Pk on a graphing calculator for large values of k.

> Evaluate the integrals.

> (A) Find the average value of each function over the indicated interval. (B) Use a graphing calculator to graph the function and its average value over the indicated interval in the same viewing window.

> Evaluate the integrals in Problem.

> Repeat Problem 53 for Data From Problem 53: Step 1 Using a transition diagram, rearrange the columns and rows of P to produce a standard form for this chain. Step 2 Find the limiting matrix for this standard form. Step 3 Using a transition diagram, rev

> Evaluate the integrals in Problem.

> Evaluate the integrals in Problem

> Evaluate the integrals in Problem.

> Use a graphing calculator to approximate the limiting matrix for the indicated standard form.

> Evaluate the integrals in Problem.

> (A) Calculate the change in F(x) from x = 10 to x = 15. (B) Graph F′(x) and use geometric formulas (see the endpapers at the back of the book) to calculate the area between the graph of F′(x) and the x axis from x = 10 to x = 15. (C) Verify that your a

> Use geometric formulas to find the unsigned area between the graph of y = ï¦(x) and the x axis over the indicated interval.

> Refer to the rectangles A, B, C, D, and E in the following figure. Which rectangles are both left and right rectangles?

> Refer to the rectangles A, B, C, D, and E in the following figure. Which rectangles are right rectangles?

> perform a mental calculation to find the answer and include the correct units. A square is circumscribed around a circle of radius 1 foot. Is the area inside the square but outside the circle less than 1 square foot?

> perform a mental calculation to find the answer and include the correct units. Find the total area enclosed by 5 non-overlapping rectangles, if each rectangle has width 3 feet and the heights of the rectangles are 2, 4, 6, 8, and 10 feet, respectively.

> Use a graphing calculator to approximate the limiting matrix for the indicated standard form.

> perform a mental calculation to find the answer and include the correct units. Find the total area enclosed by 6 non-overlapping rectangles, if each rectangle is 10 centimeters high and 3 centimeters wide.

> For the data in Problem 77, use left and right sums over three equal subintervals to approximate the area under the graph of Nâ²(x) from x = 0 to x = 6. Replace the question marks with values of L3 and R3 as appropriate: Data from Probl

> Refer to Problem 75. Use left and right sums over five equal subintervals to approximate the area under the graph of Aâ²(t) from t = 5 to t = 10. Calculate an error bound for this estimate. Data From Problem 75: The rate of healing, A&a

> For a new employee in Problem 73, use left and right sums to estimate the area under the graph of N(t) from t = 20 to t = 100. Use four equal subintervals for each. Replace the question marks with the values of L4 or R4 as appropriate:

> The left sum Ln or the right sum Rn is used to approximate the definite integral to the indicated accuracy. How large must n be chosen in each case? (Each function is increasing over the indicated interval.)

> the left sum Ln or the right sum Rn is used to approximate the definite integral to the indicated accuracy. How large must n be chosen in each case? (Each function is increasing over the indicated interval.)

> Use derivatives to determine whether ï¦ is increasing or decreasing on the given interval. Use L4 or R4, whichever is appropriate, to give an overestimate of the signed area on the given interval.

> Use L5 and R5 to approximate Compute error bounds for each. (Round answers to two decimal places.) Describe in geometric terms what the definite integral over the interval [1, 6] represents.

> Refer to the following figure showing two parcels of land along a river: Refer to Problem 61. Use R10 to estimate the combined areaÂ of both parcels, and calculate an error bound for this estimate. How many subdivisions of the baseline would

> discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a Markov chain is regular, then it is absorbing.

> could the given matrix be the transition matrix of an absorbing Markov chain?

> Discuss the validity of each statement. If the statement is always true, explain why. If it is not always true, give a counterexample. If ƒ is a decreasing function on [a, b], then the area under the graph of  is greater than the left sum Ln and less th

> Discuss the validity of each statement. If the statement is always true, explain why. If it is not always true, give a counterexample. If (x)= 2x on [0, 10] and n is a positive integer, then there is some Riemann sum Sn that equals the exact area under

> Discuss the validity of each statement. If the statement is always true, explain why. If it is not always true, give a counterexample.

> calculate the definite integral, given that

> calculate the definite integral by referring to the figure with the indicated areas.

> discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a Markov chain is absorbing, then it has a unique stationary matrix.

> calculate the definite integral by referring to the figure with the indicated areas.

> calculate the indicated Riemann sum Sn for the function (x) = x2 - 5x - 6. Partition 31, 74 into six subintervals of equal length, and let c1 = 2, c2 = 2, c3 = 4, c4 = 4, c5 = 6, and c6 = 6.

> calculate the indicated Riemann sum Sn for the function (x) = x2 - 5x - 6. Partition 30, 34 into three subintervals of equal length, and let c1 = 0.2, c2 = 1.5, and c3 = 2.8.

> calculate the indicated Riemann sum Sn for the function (x) = 25 - 3x2 . Partition 3-5, 54 into five subintervals of equal length, and for each subinterval [xk - 1, xk], let ck = (xk - 1 + xk) /2.

> calculate the indicated Riemann sum Sn for the function (x) = 25 - 3x2 . Partition 30, 124 into four subintervals of equal length, and for each subinterval [xk - 1, xk], let ck = (xk - 1 + 2xk) /3.

> Involve estimating the area under the curves in Figures AâD from x = 1 to x = 4. For each figure, divide the interval [1, 4] into three equal subintervals. Compute error bounds for L3 and R3 found in Problem 18 for both figures.

> discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a Markov chain has exactly three states, one nonabsorbing and two absorbing, then it is an absorbing chain.

> Involve estimating the area under the curves in Figures A–D from x = 1 to x = 4. For each figure, divide the interval [1, 4] into three equal subintervals. Replace the question marks with L3 and R3 as appropriate. Explain your choice.

> Involve estimating the area under the curves in Figures A–D from x = 1 to x = 4. For each figure, divide the interval [1, 4] into three equal subintervals. Using the results of Problem 16, compute L3 and R3 for Figure C and for Figure D.

> Involve estimating the area under the curves in Figures A–D from x = 1 to x = 4. For each figure, divide the interval [1, 4] into three equal subintervals. Draw in left and right rectangles for Figures C and D.

> Refer to the rectangles F, G, H, I, and J in the following figure. Which rectangles are neither left nor right rectangles?

> Refer to the rectangles F, G, H, I, and J in the following figure. Which rectangles are left rectangles?

> Find the general or particular solution, as indicated, for each first-order differential equation.

> Express the relationship between ï¦= (x) and ï¦(x) in words, and write a differential equation that ï¦(x) satisfies. For example, the derivative of ï¦(x) = e3x is 3 times ï&#1

> discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a Markov chain has exactly two states and at least one absorbing state, then it is an absorbing chain.

> The WeberâFechner law concerns a personâs sensed perception of various strengths of stimulation involving weights, sound, light, shock, taste, and so on. One form of the law states that the rate of change of sensed sen

> For a person learning to type, the number N of words per minute that the person could type after t hours of practice was given by the limited growth function N = 1001(1 - e-0.02t ) What is the rate of improvement after 10 hours of practice? After 40 ho

> Many countries have banned the use of the insecticide DDT because of its long-term adverse effects. Five years after a particular country stopped using DDT, the amount of DDT in the ecosystem had declined to 70% of the amount present at the time of the b

> A community of 10,000 people is homogeneously mixed. One person who has just returned from another community has influenza. Assume that the home community has not had influenza shots and all are susceptible. One mathematical model assumes that influenza

> Under certain assumptions, the blood pressure P in the largest artery in the human body (the aorta) changes between beats with respect to time t according to where a is a constant. Find P = P(t) that satisfies both conditions

> A company is trying to expose a new product to as many people as possible through online ads. Suppose that the rate of exposure to new people is proportional to the number of those who have not seen the product out of L possible viewers (limited growth).

> The marginal price dp/dx at x units of supply per day is proportional to the price p. There is no supply at a price of $20 per unit [p(0) = 20], and there is a daily supply of 40 units at a price of $23.47 per unit [p(40) = 23.47]. (A) Find the price–su

> Find the amount A in an account after t years if

> Refer to Problem 75. Explain why the world population function Q(t) does not satisfy an exponential growth law. Data from Problem 75: Let Q(t) denote the population of the world at time t. In 1999, the world population was 6.0 billion and increasing at

> Use the limiting matrix P found for each transition matrix P in Problems 29â34 to determine the long-run behavior of the successive state matrices for the indicated initial-state matrices

> Find the value of t for which the logistic function is equal to M/2.

> use a graphing calculator to graph the given examples of the various cases in Table 1.

Question: use derivatives to determine whether f is