All Matches
Solution Library
Expert Answer
Textbooks
Search Textbook questions, tutors and Books
Oops, something went wrong!
Change your search query and then try again
Toggle navigation
FREE Trial
S
Books
FREE
Tutors
Study Help
Expert Questions
Accounting
General Management
Mathematics
Finance
Organizational Behaviour
Law
Physics
Operating System
Management Leadership
Sociology
Programming
Marketing
Database
Computer Network
Economics
Textbooks Solutions
Accounting
Managerial Accounting
Management Leadership
Cost Accounting
Statistics
Business Law
Corporate Finance
Finance
Economics
Auditing
Ask a Question
Search
Search
Sign In
Register
study help
mathematics
applied calculus
Questions and Answers of
Applied Calculus
The graph of f(x) is given in Figure 2.26. Draw tangent lines to the graph at x = −2, x = −1, x = 0, and x = 2. Estimate f'(−2), f'(−1), f'(0), and f'(2). 4 2 1 -4 -3 -2 -1 0 1 2 Figure
Write the Leibniz notation for the derivative of the given function and include units.The distance to the ground, D, in feet, of a skydiver is a function of the time t in minutes since the skydiver
Refer to the graph in Figure 2.11.Does each quantity appear to be positive, negative, or zero?(a) f(−2) (b) f(0) (c) f(4)(d) f(5) (e) f'(−2) (f) f'(2)(g) f'(4) (h) f'(5)
You put a yam in a hot oven, maintained at a constant temperature of 200◦C. As the yam picks up heat from the oven, its temperature rises.(a) Draw a possible graph of the temperature T of the yam
It costs $4800 to produce 1295 items and it costs $4830 to produce 1305 items. What is the approximate marginal cost at a production level of 1300 items?
For the function g(x) graphed in Figure 2.45, are the following nonzero quantities positive or negative?(a) g'(0) (b) g"(0) 4 2 1 -4 -3 -2 -1 0 1 2 3 4 Figure 2.45 X
On Figure 2.73, mark lengths that represent the quantities in parts (a)–(e). (Pick any ℎ, with ℎ > 0.)(a) a + ℎ (b) ℎ (c) f(a)(d) f(a + ℎ)(e) f(a+ℎ)−f(a)(f) Using your
The graph of f(x) is given in Figure 2.27. Estimate f'(1), f'(2), f'(3), f'(4), and f'(5). 6 5 4 3 2 1 f(x) 1 2 3 4 Figure 2.27 5 6 X
Write the Leibniz notation for the derivative of the given function and include units.The cost, C, of a steak, in dollars, is a function of the weight, W, of the steak, in pounds.
Alone in your dim, unheated room, you light a single candle rather than curse the darkness. Depressed with the situation, you walk directly away from the candle, sighing. The temperature (in degrees
Refer to the graph in Figure 2.11.Which of the two quantities appears to be larger?(a) f(1) or f(2) (b) f(5) or f(6)(c) f(3) or f(4) (d) f'(−2) or f'(2)(e) f'(4) or f'(5) (f)
The function C(q) gives the cost in dollars to produce q barrels of olive oil.(a) What are the units of marginal cost?(b) What is the practical meaning of the statement MC = 3 for q = 100?
At one of the labeled points on the graph in Figure 2.46 both dy∕dx and d2y∕dx2 are negative. Which is it? y A B C D E Figure 2.46 - x
On Figure 2.74, mark lengths that represent the quantities in parts (a)–(e). (Pick any ℎ, with ℎ > 0.)(a) a + ℎ(b) ℎ(c) f(a)(d) f(a + ℎ)(e) f(a+ℎ)−f(a)(f) Using your answers to
Write the Leibniz notation for the derivative of the given function and include units.The number, N, of gallons of gas left in a gas tank is a function of the distance, D, in miles, the car has been
For Problem graph the derivative of the given function. -4 4 -4 4+
Chlorofluorocarbons (CFCs) were used as propellants in spray cans until their buildup in the atmosphere started destroying the ozone, which protects us from ultraviolet rays. Since the 1987 Montreal
In Figure 2.61, estimate the marginal revenue when the level of production is 600 units and interpret it. 20,000 10,000 $ GA 0 600 Figure 2.61 R(q) 9
For the expressions in Problems(a) What is the result when we substitute ℎ = 0?(b) Find the values when we substitute ℎ = 0.1, ℎ = 0.01, ℎ = 0.001, and ℎ = 0.0001.(c) Use the results of
Write the Leibniz notation for the derivative of the given function and include units.An employee’s pay, P, in dollars, for a week is a function of the number of hours worked, H.
For Problem graph the derivative of the given function. -4 T 4 -4 4 x
Which of the functions A, B, C, D in Figure 2.12 satisfy the given condition?f(4) < 0 (A) (C) y y +N 2 -2. + 4/6 X (B) (D) Figure 2.12 y y +N ++ 4 ए — x 6 4 6 X
In Figure 2.62, is marginal cost greater at q = 5 or at q = 30? At q = 20 or at q = 40? Explain. 500 400 300 200 100 s C(q) 10 20 30 40 50 Figure 2.62 9
Give the signs of the first and second derivatives for the function. Each derivative is either positive everywhere, zero everywhere, or negative everywhere. 1 f(x) X
For the expressions in Problems(a) What is the result when we substitute ℎ = 0?(b) Find the values when we substitute ℎ = 0.1, ℎ = 0.01, ℎ = 0.001, and ℎ = 0.0001.(c) Use the results of
The time for a chemical reaction, T (in minutes), is a function of the amount of catalyst present, a (in milliliters), so T = f(a).(a) If f(5) = 18, what are the units of 5?What are the units of 18?
Graph the derivative of the given function. -4 4." -4 4 X
Which of the functions A, B, C, D in Figure 2.12 satisfy the given condition?f'(2) > 0 (A) (C) y y +N 2 -2. + 4/6 X (B) (D) Figure 2.12 y y +N ++ 4 ए — x 6 4 6 X
Use the graphs in Figure 1.90.Estimate f(f(2)). 2 2 -f(x)- 4 6 X 4 2 Figure 1.90 2 -g(x)- 4 6 + x
The specific heat, s, of an element is the number of calories of heat required to raise the temperature of one gram of the element by one degree Celsius. Use the following table to decide if s is
Find a possible formula for the graph. -1 y 5 x
In Problems 25–28, a quantity P is an exponential function of time t. Use the given information about the function P = P0at to:(a) Find values for the parameters a and P0. (b) State the
A corporate office provides the demand curve in Figure 1.63 to its ice cream shop franchises. At a price of $1.00 per scoop, 240 scoops per day can be sold.(a) Estimate how many scoops could be sold
Table 1.17 gives sales of Pepsico, which operates two major businesses: beverages (including Pepsi) and snack foods.(a) Find the change in sales between 2003 and 2015. (b) Find the average rate
Use Figure 1.94 to graph the function.y = f(x) + 1 -3 -2 -1 y y = f(x) 12 Figure 1.94 LX 3
One of the main contaminants of a nuclear accident, such as that at Chernobyl, is strontium-90, which decays exponentially at a rate of approximately 2.4% per year. (a) Write the percent of
With time, t, in years since the start of 1980, textbook prices have increased at 6.7% per year while inflation has been 3.3% per year. Assume both rates are continuous growth rates. (a) Find a
In 2014, the populations of China and India were approximately 1.355 and 1.255 billion people, respectively. However, due to central control the annual population growth rate of China was 0.44% while
The US Consumer Price Index (CPI) is a measure of the cost of living. The inflation rate is the annual relative rate of change of the CPI. Use the January data in Table 1.24 to estimate the inflation
The functions r = f(t) and V = g(r) give the radius and the volume of a commercial hot air balloon being inflated for testing. The variable t is in minutes, r is in feet, and V is in cubic feet. The
During 2008 the US economy stopped growing and began to shrink. Table 1.25 gives quarterly data on the US Gross Domestic Product (GDP), which measures the size of the economy.(a) Estimate the
The functions r = f(t) and V = g(r) give the radius and the volume of a commercial hot air balloon being inflated for testing. The variable t is in minutes, r is in feet, and V is in cubic feet. The
An alternative to petroleum-based diesel fuel, biodiesel, is derived from renewable resources such as food crops, algae, and animal oils. The table shows the recent annual percent growth in US
The functions r = f(t) and V = g(r) give the radius and the volume of a commercial hot air balloon being inflated for testing. The variable t is in minutes, r is in feet, and V is in cubic feet. The
Hydroelectric power is electric power generated by the force of moving water. Figure 1.48 shows the annual percent growth in hydroelectric power consumption by the US industrial sector between 2006
Cyanide is used in solution to isolate gold in a mine. This may result in contaminated groundwater near the mine, requiring the poison be removed, as in the following table, where t is in years since
Solar panels are arrays of photovoltaic cells that convert solar radiation into electricity. The table shows the annual percent change in the US price per watt of a solar panel. (a) Find the
School organizations raise money by selling candy door-to-door. When the price is $1 a school organization sells 2765 candies and when the price goes up to $1.25 the quantity of candy sold drops down
The functions r = f(t) and V = g(r) give the radius and the volume of a commercial hot air balloon being inflated for testing. The variable t is in minutes, r is in feet, and V is in cubic feet. The
On January 22, 2017, the cost to mail a letter in the US was raised from 47 cents to 49 cents. Find the relative change in the cost.
You are buying a car that comes with a one-year warranty and are considering whether to purchase an extended warranty for $375. The extended warranty covers the two years immediately after the
Morphine, a pain-relieving drug, is administered to a patient intravenously starting at 8 am. The drug saturation curve Q = f(t) in Figure 1.97 gives the quantity, Q, of morphine in the blood t hours
You are considering whether to buy or lease a machine whose purchase price is $12,000. Taxes on the machine will be $580 due in one year, $464 due in two years, and $290 due in three years. If you
Find the relative change of a population if it changes (a) From 1000 to 2000 (b) From 2000 to 1000 (c) From 1,000,000 to 1,001,000
Use Figure 1.95 to graph the function. y = 2f(x) − 1 -5 -4 -3 -2 -1 2 y 1 Figure 1.95 2 y = f(x) 3 درا 4 5 X
Use Figure 1.95 to graph the function. y = 2f(x) -5 -4 -3 -2 -1 2 y 1 Figure 1.95 2 y = f(x) 3 درا 4 5 X
The population of a city is 50,000 in 2014 and is growing at a continuous rate of 4.5% per year. (a) Give the population of the city as a function of the number of years since 2014. Sketch a
(a) Use the Rule of 70 to predict the doubling time of an investment which is earning 8% interest per year. (b) Find the doubling time exactly, and compare your answer to part (a).
Find the relative, or percent, change.W changes from 0.3 to 0.05
During a recession a firm’s revenue declines continuously so that the revenue, R (measured in millions of dollars), in t years’ time is given by R = 5e−0.15t.(a) Calculate the current revenue
Use Figure 1.95 to graph the function. y = f(x) + 2 -5 -4 -3 -2 -1 2 y 1 Figure 1.95 2 y = f(x) 3 درا 4 5 X
A car starts slowly and then speeds up. Eventually the car slows down and stops. Graph the distance that the car has traveled against time.
Experiments suggest that the male maximum heart rate (the most times a male’s heart can safely beat in a minute) decreases by 9 beats per minute during the first 21 years of his life, and by 26
The gross world product is W = 74.31(1.029)t, where W is in trillions of dollars and t is years since 2013. Find a formula for gross world product using a continuous growth rate.
Concern biodiesel, a fuel derived from renewable resources such as food crops, algae, and animal oils. The table shows the percent growth over the previous year in US biodiesel consumption.(a)
Ask you to plot graphs based on the following story: “As I drove down the highway this morning, at first traffic was fast and uncongested, then it crept nearly bumper to-bumper until we passed an
In November 2010, a “tiger summit” was held in St. Petersburg, Russia. In 1900, there were 100,000 wild tigers worldwide; in 2010 the number was 3200. (a) Assuming the tiger population has
A picture supposedly painted by Vermeer (1632–1675) contains 99.5% of its carbon-14 (half-life 5730 years). From this information decide whether the picture is a fake. Explain your reasoning.
In 2010, there were about 246 million vehicles (cars and trucks) and about 308.7 million people in the US. The number of vehicles grew 15.5% over the previous decade, while the population has been
Figure 1.96 shows the concentration of a drug in the body, f(t) = a − bekt, over time, t:(a) What does the constant a represent in this context? (b) What is the sign of the constant
You win $38,000 in the state lottery to be paid in two installments—$19,000 now and $19,000 one year from now. A friend offers you $36,000 in return for your two lottery payments. Instead of
Use Figure 1.95 to graph the function. y = 2 − f(x) -5 -4 -3 -2 -1 2 y 1 Figure 1.95 2 y = f(x) 3 درا 4 5 X
Which relative change is bigger in magnitude? Justify your answer.An increase in sales from $100,000 to $500,000; an increase in sales from $20,000,000 to $20,500,000.
Big Tree McGee is negotiating his rookie contract with a professional basketball team. They have agreed to a three-year deal which will pay Big Tree a fixed amount at the end of each of the three
Which relative change is bigger in magnitude? Justify your answer.An increase in class size from 5 to 10; an increase in class size from 30 to 50.
A company is considering whether to buy a new machine, which costs $97,000. The cash flows (adjusted for taxes and depreciation) that would be generated by the new machine are given in the following
Which relative change is bigger in magnitude? Justify your answer.The change in the US population from 5.2 million to 7.2 million from 1800 to 1810; the change in the US population from 151.3 to
The concentration of the car exhaust fume nitrous oxide, NO2, in the air near a busy road is a function of distance from the road. The concentration decays exponentially at a continuous rate of 2.54%
Use Figure 1.95 to graph the function. y = −3f(x) -5 -4 -3 -2 -1 2 y 1 Figure 1.95 2 y = f(x) 3 درا 4 5 X
A person is to be paid $2000 for work done over a year. Three payment options are being considered. Option 1 is to pay the $2000 in full now. Option 2 is to pay $1000 now and $1000 in a year. Option
Which relative change is bigger in magnitude? Justify your answer.The change in the Dow Jones average from 164.6 to 77.9 in 1931; the change in the Dow Jones average from 13,261.8 to 8776.4 in
Use Figure 1.95 to graph the function. y = f(x − 1) -5 -4 -3 -2 -1 2 y 1 Figure 1.95 2 y = f(x) 3 درا 4 5 X
For children and adults with diseases such as asthma, the number of respiratory deaths per year increases by 0.33% when pollution particles increase by a microgram per cubic meter of air.(a) Write a
A business associate who owes you $3000 offers to pay you $2800 now, or else pay you three yearly installments of $1000 each, with the first installment paid now. If you use only financial reasons to
Find the relative, or percent, change.R changes from 50 to 47
Hydroelectric power is electric power generated by the force of moving water. The table shows the annual percent change in hydroelectric power consumption by the US industrial sector. (a)
The demand and supply curves for a product are given in terms of price, p, byq = 2500 − 20p and q = 10p − 500.(a) Find the equilibrium price and quantity. Represent your answers on a graph.(b) A
Find the present value of an $8000 payment to be made in 5 years. The interest rate is 4% per year compounded continuously.
An Australian study found that, if other factors are constant (education, experience, etc.), taller people receive higher wages for the same work. The study reported a “height premium” for men of
The population of the world can be represented by P = 7.32(1.0109)t, where P is in billions of people and t is years since 2015. Find a formula for the population of the world using a continuous
Concern wind power, which has been used for centuries to propel ships and mill grain. Modern wind power is obtained from windmills that convert wind energy into electricity. Figure 1.74 shows the
The demand and supply curves are given by q = 100 − 2p and q = 3p − 50, respectively; the equilibrium price is $30 and the equilibrium quantity is 40 units. A sales tax of 5% is imposed on the
Find the present value of a $20,000 payment to be made in 10 years. Assume an interest rate of 3.2% per year compounded continuously.
A fishery stocks a pond with 1000 young trout. The number of trout t years later is given by P(t) = 1000e−0.5t.(a) How many trout are left after six months? After 1 year? (b) Find P(3) and
Find the relative, or percent, change.B changes from 12,000 to 15,000
Concern wind power, which has been used for centuries to propel ships and mill grain. Modern wind power is obtained from windmills that convert wind energy into electricity. Figure 1.74 shows the
Answer the questions in Problem 44, assuming that the 5% sales tax is imposed on the supplier instead of the consumer.Data from in Problem 44The demand and supply curves are given by q = 100 − 2p
Interest is compounded annually. Consider the following choices of payments to you: Choice 1: $1500 now and $3000 one year from now Choice 2: $1900 now and $2500 one year from now (a)
The Hershey Company is the largest US producer of chocolate. In 2011, annual net sales were 6.1 billion dollars and were increasing at a continuous rate of 7% per year. (a) Write a formula for
Find the relative, or percent, change. S changes from 400 to 450
Showing 1100 - 1200
of 5532
First
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Last