Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The theoretical probability of an event is less than or equal to its empirical probability.
> Referring to Problem 33, in how many years will the $10,000 be due in order for its present value to be $5,000? Data from Problem 33: Solving A = Pert for P, we obtain P = Ae-rt which is the present value of the amount A due in t years if money earns in
> A family paid $99,000 cash for a house. Fifteen years later, the house was sold for $195,000. If interest is compounded continuously, what annual nominal rate of interest did the original $99,000 investment earn?
> A note will pay $50,000 at maturity 5 years from now. How much should you be willing to pay for the note now if money is worth 6.4% compounded continuously?
> Provident Bank also offers a 3-year CD that earns 1.64% compounded continuously. (A) If $10,000 is invested in this CD, how much will it be worth in 3 years? (B) How long will it take for the account to be worth $11,000?
> Compute the odds in favor of obtaining. A number divisible by 3 in a single roll of a die
> Without using a calculator, determine which event, E or F, is more likely to occur.
> It can be shown that for any real number s. Illustrate this equation graphically for s = 2 by graphing in the same viewing window, for 1 ≤ n ≤ 50.
> Use a calculator and a table of values to investigate Do you think this limit exists? If so, what do you think it is?
> use a calculator to complete each table to five decimal places.
> solve for t or r to two decimal places. 3 = e20r
> solve for t or r to two decimal places. 3 = e0.08t
> solve for t or r to two decimal places. 2 = e18r
> solve for t or r to two decimal places. 2 = e0.09t
> If $4,000 is invested at 8% compounded continuously, graph the amount in the account as a function of time for a period of 6 years.
> Use a calculator to evaluate A to the nearest cent A = $10,000e0.1t for t = 10, 20, and 30
> solve for the variable to two decimal places. 4,840 = 3,750e4.25r
> An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space shown in Figure 2 (page 398) and, assuming each simple event is as likely as any other, find the probability of the sum of the dots ind
> solve for the variable to two decimal places. 10,000 = 7,500e0.085t
> let C(x) = 10,000 + 150x - 0.2x2 be the total cost in dollars of producing x bicycles Find the cost of producing the 200th bicycle.
> let C(x) = 10,000 + 150x - 0.2x2 be the total cost in dollars of producing x bicycles Find the total cost of producing 199 bicycles.
> let C(x) = 10,000 + 150x - 0.2x2 be the total cost in dollars of producing x bicycles Find the total cost of producing 100 bicycles.
> Table 2 contains price–demand and total cost data for the production of treadmills, where p is the wholesale price (in dollars) of a treadmill for an annual demand of x treadmills and C is the total cost (in dollars) of producing x tre
> The price–demand equation and the cost function for the production of handwoven silk scarves are given, respectively, by p = 60 - 21x and C(x)= 3,000 + 5x where x is the number of scarves that can be sold at a price of $p per unit and C(x) is the total
> The total cost and the total revenue (in dollars) for the production and sale of x hair dryers are given, respectively, by (A) Find the value of x where the graph of R(x) has a horizontal tangent line. (B) Find the profit function P(x). (C) Find the
> The company in Problem 47 is also planning to manufacture and market a four-slice toaster. For this toaster, the research department’s estimates are a weekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a pr
> The price–demand equation and the cost function for the production of HDTVs are given, respectively, by x = 9,000 - 30p and C(x) = 150,000 + 30x where x is the number of HDTVs that can be sold at a price of $p per TV and C(x) is the total cost (in dolla
> The price p (in dollars) and the demand x for a particular steam iron are related by the equation x = 1,000 - 20p (A) Express the price p in terms of the demand x, and find the domain of this function. (B) Find the revenue R(x) from the sale of x steam
> Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If E and F are mutually exclusive events, then E and F are complementary.
> The total profit (in dollars) from the sale of x gas grills is P(x) = 20x - 0.02x2 - 320 0 ≤ x ≤ 1,000 (A) Find the average profit per grill if 40 grills are produced. (B) Find the marginal average profit at a production level of 40 grills and interp
> The total profit (in dollars) from the sale of x cameras is P(x) = 12x - 0.02x2 - 1,000 0 ≤ x ≤ 600 Evaluate the marginal profit at the given values of x, and interpret the results. (A) x = 200 (B) x = 350
> The total profit (in dollars) from the sale of x calendars is P(x) = 22x - 0.2x2 - 400 0 ≤ x ≤ 100 (A) Find the exact profit from the sale of the 41st calendar. (B) Use the marginal profit to approximate the profit from the sale of the 41st calendar.
> The total cost (in dollars) of printing x board games is C(x) = 10,000 + 20x (A) Find the average cost per unit if 1,000 board games are produced. (B) Find the marginal average cost at a production level of 1,000 units and interpret the results. (C) U
> The total cost (in dollars) of producing x electric guitars is C(x) = 1,000 + 100x - 0.25x2 (A) Find the exact cost of producing the 51st guitar. (B) Use marginal cost to approximate the cost of producing the 51st guitar.
> Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. Marginal average cost is equal to average marginal cost.
> Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a price–demand equation is linear, then the marginal revenue function is linear.
> find the indicated function if cost and revenue are given by C(x) = 145 + 1.1x and R(x) = 5x - 0.02x2 , respectively. Marginal average Profit function
> find the indicated function if cost and revenue are given by C(x) = 145 + 1.1x and R(x) = 5x - 0.02x2 , respectively. Marginal Profit function
> find the indicated function if cost and revenue are given by C(x) = 145 + 1.1x and R(x) = 5x - 0.02x2 , respectively. Marginal average revenue function
> An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space shown in Figure 2 (page 398) and, assuming each simple event is as likely as any other, find the probability of the sum of the dots ind
> find the indicated function if cost and revenue are given by C(x) = 145 + 1.1x and R(x) = 5x - 0.02x2 , respectively. Average revenue function
> find the marginal profit function if the cost and revenue, respectively, are those in the indicated problems. Problem 12 and Problem 16 Data from Problem 12 and Problem 16:
> find the marginal profit function if the cost and revenue, respectively, are those in the indicated problems. Problem 10 and Problem 14 Data from Problem 10 and Problem 14:
> find the marginal revenue function.
> find the marginal revenue function.
> find the marginal cost function. C(x ) = 640 + 12x - 0.1x2
> find the marginal cost function. C(x ) = 2,700 + 6x
> let C(x) = 10,000 + 150x - 0.2x2 be the total cost in dollars of producing x bicycles Find the average cost per bicycle of producing 200 bicycles.
> let g(x) = x2 and find the given values without using a calculator
> let  (x) = 0.1x + 3 and find the given values without using a calculator
> let  (x) = 0.1x + 3 and find the given values without using a calculator
> If a person learns y items in x hours, as given approximately by what is the approximate increase in the number of items learned when x changes from 1 to 1.1 hours? From 4 to 4.1Â hours?
> One hour after x milligrams of a particular drug are given to a person, the change in body temperature T (in degrees Fahrenheit) is given by Approximate the changes in body temperature produced by the following changes in drug dosages: (A) From 2 to 2.
> An egg of a particular bird is nearly spherical. If the radius to the inside of the shell is 5 millimeters and the radius to the outside of the shell is 5.3 millimeters, approximately what is the volume of the shell? Remember that:
> A company manufactures and sells x televisions per month. If the cost and revenue equations are what will the approximate changes in revenue and profit be if production is increased from 1,500 to 1,510? From 4,500 to 4,510?
> Suppose that the daily demand (in pounds) for chocolate candy at $x per pound is given by D = 1,000 - 40x2 1 ≤ x ≤ 5 If the price is increased from $3.00 per pound to $3.20 per pound, what is the approximate change in demand?
> Find dy and ∆y for y = 590 / √x, x = 64, and ∆x = dx = 1.
> Find dy if y = (2x2 – 4) √x.
> discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. Suppose that y = (x) defines a function whose domain is the set of all real numbers. If every increment at x = 2 is equal to 0, then (x
> discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If the graph of the function y = (x) is a parabola, then the functions ∆y and dy (of the independent variable ∆x = dx) for (x) at x = 0
> An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space shown in Figure 2 (page 398) and, assuming each simple event is as likely as any other, find the probability of the sum of the dots ind
> (A) Find ∆y and dy for the function f at the indicated value of x. (B) Graph ∆y and dy from part (A) as functions of ∆x. (C) Compare the values of ∆y and dy from part (A) at the in
> (A) Find ∆y and dy for the function f at the indicated value of x. (B) Graph ∆y and dy from part (A) as functions of ∆x. (C) Compare the values of ∆y and dy from part (A) at the in
> A sphere with a radius of 5 centimeters is coated with ice 0.1 centimeter thick. Use differentials to estimate the volume of the ice.
> evaluate dy and ∆y for each function for the indicated values.
> evaluate dy and ∆y for each function for the indicated values.
> find dy for each function.
> find dy for each function. y = (2x + 3)2
> find the indicated quantities for y = (x) = 3x2 .
> find dy for each function.
> find dy for each function.
> Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If the odds for E are a: b, then the odds against E are b: a.
> find dy for each function.
> find the indicated quantities for y =  (x) = 5x2 .
> find the indicated quantities for y =  (x) = 5x2 .
> find the indicated quantities for y =  (x) = 5x2 .
> let g(x) = x2 and find the given values without using a calculator
> write the expression in the form xn .
> write the expression in the form xn .
> write the expression in the form xn .
> write the expression in the form xn .
> If a person learns y items in x hours, as given by find the rate of learning at the end of (A) 1 hour (B) 8 hours
> An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space shown in Figure 2 (page 398) and, assuming each simple event is as likely as any other, find the probability of the sum of the dots ind
> A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The concentration C(x), in parts per million, is given approximately by where x is the distance from the plant in miles. Find the instantaneous rate of change of c
> The percentages of female high school graduates who enrolled in college are given in the third column of Table 1. (A) Let x represent time (in years) since 1970, and let y represent the corresponding percentage of female high school graduates who enroll
> Suppose that, in a given gourmet food store, people are willing to buy x pounds of chocolate candy per day at $p per quarter pound, as given by the price– demand equation This function is graphed in the figure. Find the demand and the
> A company’s total sales (in millions of dollars) t months from now are given by S(t) = 0.015t4 + 0.4t3 + 3.4t2 + 10t - 3 (A) Find S′(t). (B) Find S(4) and S′(4) (to two decimal places). Write a brief verbal interpretation of these results. (C) Find S(8
> Let (x) = u(x) - v(x), where u′(x) and v′(x) exist. Use the four-step process to show that = (x) = u′(x) - v′(x).
> Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The derivative of a constant times a function is 0.
> Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The derivative of a quotient is the quotient of the derivatives.
> Find the indicated derivatives.
> Find the indicated derivatives.
> Find the indicated derivatives. y′ if y = (2x – 5)2
> Compute the probability of event E if the odds in favor of E are. Answer:
> Can a cubic polynomial function have more than two horizontal tangents? Explain.
> Now that you know how to find derivatives, explain why it is no longer necessary for you to memorize the formula for the x coordinate of the vertex of a parabola.
> Require the use of a graphing calculator. For each problem, find ’(x) and approximate (to four decimal places) the value(s) of x where the graph of f has a horizontal tangent line.
> Require the use of a graphing calculator. For each problem, find ’(x) and approximate (to four decimal places) the value(s) of x where the graph of f has a horizontal tangent line.
> Require the use of a graphing calculator. For each problem, find ’(x) and approximate (to four decimal places) the value(s) of x where the graph of f has a horizontal tangent line.
> Require the use of a graphing calculator. For each problem, find ’(x) and approximate (to four decimal places) the value(s) of x where the graph of f has a horizontal tangent line.
> If an object moves along the y axis (marked in feet) so that its position at time x (in seconds) is given by the indicated functions. Find (A) The instantaneous velocity function v = ’(x) (B) The velocity when x = 0
