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mathematics
calculus with applications
Questions and Answers of
Calculus With Applications
Give the domain of each function defined as follows. f(x) = -8 x² - 36
Give the domain of each function defined as follows. f(x) 2 1-x²
Give the domain of each function defined as follows.ƒ(x) = (3x + 5)1/2
Give the domain of each function defined as follows.ƒ(x) = (x - 3)1/2
Give the domain of each function defined as follows.ƒ(x) = |3x – 6|
Give the domain of each function defined as follows.ƒ(x) = √4 - x2
Give the domain of each function defined as follows.ƒ(x) = (x + 3)2
Give the domain of each function defined as follows.ƒ(x) = x4
Give the domain of each function defined as follows.ƒ(x) = 2x + 3
Give the domain of each function defined as follows.ƒ(x) = 2x
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.y = -4x2
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.y = x2
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.y = (x - 2)(x + 2)
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.y = x(x + 2)
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.6x - y = -1
Which of the following rules define y as a function of x? X 9 4 1 0 1 4 9 y 32 1 0 -1 -2 -3
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.2y - x = 5
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.y = -3x + 9
Which of the following rules define y as a function of x? 82 23 X 17. Y 27 .6 93 14
List the ordered pairs obtained from each equation, given {-2, - 1, 0, 1, 2, 3} as the domain. Graph each set of ordered pairs. Give the range.y = 2x + 3
Which of the following rules define y as a function of x? X V 9 2 4 1 1 0 0 -1 1 -2 4 -3 9 3 32 نا انا
Which of the following rules define y as a function of x?x = y2 + 4
Which of the following rules define y as a function of x?x = y
Which of the following rules define y as a function of x? 12 54 32 9. 27 X Y 69 101 43 18
Which of the following rules define y as a function of x?y = √x
Which of the following rules define y as a function of x?y = x3 + 2
The function ƒ(x) = 0 is both even and odd.Determine whether each statement is true or false, and explain why.
The range of the function ƒ(x) = 1/x is all real numbers.Determine whether each statement is true or false, and explain why.
The equation y = x4 does not define a function because it assigns the number 16 to two different x-values, 2 and -2.Determine whether each statement is true or false, and explain why.
A function is a rule that assigns one or more elements from one set to each element in another set.Determine whether each statement is true or false, and explain why.
In Exercises, find a linear cost function.Twelve units cost $445; 50 units cost $1585.
To manufacture x thousand computer chips requires fixed expenditures of $352 plus $42 per thousand chips. Receipts from the sale of x thousand chips amount to $130 per thousand.(a) Find the linear
For the lines in exercises which of the following is closest to the slope of the line? (a) 1 (b) 2 (c) 3 (d) 21 (e) 22(f) - 3 2 + + 2 X
In exercises, estimate the slope of the lines. -2- 2 x
You are the manager of a firm. You are considering the manufacture of a new product, so you ask the accounting department for cost estimates and the sales department for sales estimates. After you
Graph each linear equation defined as follows.x + 3y = 0
In exercises, estimate the slope of the lines. 2 2 ++
You are the manager of a firm. You are considering the manufacture of a new product, so you ask the accounting department for cost estimates and the sales department for sales estimates. After you
The United States is China’s largest export market. Imports from China have grown from about $100 billion in 2000 to $540 billion in 2018. This growth has been approximately linear.(a) Determine a
You are the manager of a firm. You are considering the manufacture of a new product, so you ask the accounting department for cost estimates and the sales department for sales estimates. After you
U.S. exports to China have grown (although at a slower rate than imports) since 2000. In 2000, about $16 billion of goods were exported to China. By 2018, this amount had grown to $120 billion. This
You are the manager of a firm. You are considering the manufacture of a new product, so you ask the accounting department for cost estimates and the sales department for sales estimates. After you
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Vertical, through 1-6, 52
Suppose that the demand and price for a certain model of a youth wristwatch are related by p = D(q) = 16 - 1.25q, where p is the price (in dollars) and q is the quantity demanded (in hundreds). Find
The following data give the expected points for a football team with first down and 10 yards to go from various points on the field.(a) Calculate the correlation coefficient. Does there appear to be
To show that two perpendicular lines, neither of which is vertical, have slopes with a product of -1, go through the following steps. Let line L1 have equation y = m1 x + b1 , and let L2 have
Consider the equation(a) Show that this equation represents a line by writing it in the form y = mx + b.(b) Find the x- and y-intercepts of this line.(c) Explain in your own words why the equation in
In recent decades, the median income for all U.S. households has increased in a roughly linear manner. In 1990, the median income was $29,943. By 2018, it had risen to $63,179. Source: U.S. Census
Suppose that the fixed cost for a product is $400 and the break-even quantity is 80. Find the marginal profit (the slope of the linear profit function).
The supply and demand for fresh jumbo lump crabmeat in a local fish store are related by the equationsSupply: p = S(q) = 4q + 10andDemand: p = D(q) = 40 - 4q,where p represents the price in dollars
Suppose that the fixed cost for a product is $650 and the break-even quantity is 25. Find the marginal profit (the slope of the linear profit function).
Graph each equation.y = x - 1
Deer ticks are of concern because they can carry the parasite that causes Lyme disease. One study found a relationship between the density of acorns produced in the fall and the density of deer tick
In Exercises, find a linear cost function.Eight units cost $300; fixed cost is $60.
Graph each equation.y = 4x + 5
The U.S. Centers for Disease Control and Prevention projects that tobacco could soon be the leading cause of death in the world. In 1990, 35 million years of healthy life were lost globally due to
In Exercises, find a linear cost function.Fixed cost is $2000; 36 units cost $8480.
Graph each equation.y = -4x + 9
Use the formula for conversion between Fahrenheitand Celsius derived in Example 8 to convert each temperature.(a) 58°F to Celsius (b) -20°F to Celsius(c) 50°C to Fahrenheit
Graph each equation.y = -6x + 12
You may have heard that the average temperature of the human body is 98.6°. Recent experiments show that the actual figure is closer to 98.2°. The figure of 98.6 comes from experiments done by Carl
Find the temperature at which the Celsius and Fahrenheit temperatures are numerically equal.
In Exercises, find a linear cost function.Thirty units cost $1500; 120 units cost $5640.
Graph each equation.2x - 3y = 12
A report estimated the cost to build a new 30% carbon sequestration coal-generated electricity plant with a capacity of 650 MW to be $3.308 billion, with a marginal cost of $7.17 for each MWh of
The cost of producing x cartons of CDs is C(x) dollars, where C(x) = 200x + 1000. The CDs sell for $400 per carton.(a) Find the break-even quantity.(b) What revenue will the company receive if it
Graph each equation.3x - y = -9
The cost function for flavored coffee at an upscale coffeehouse is given in dollars by C(x) = 3x + 160, where x is in pounds. The coffee sells for $7 per pound.(a) Find the break-even quantity.(b)
Graph each equation.3y - 7x = -21
The average new car cost (in dollars) from 2002 to 2018 is given in the table.(a) Find a linear equation for the average new car cost in terms of t, the number of years since 2000, using the data for
Graph each equation.5y + 6x = 11
The U.S. per capita consumption (in pounds) of beef, pork, and chicken for 2000 and 2016 is given in the following table. Assume that the changes in consumption are approximately linear.(a) Determine
Graph each equation.y = -2
In general, people tend to live longer in countries that have a greater supply of food. Listed in the table below is the 2013 daily calorie supply and 2010–2015 life expectancy at birth for 10
Grandfather clocks use pendulums to keep accurate time. The relationship between the length of a pendulum L and the time T for one complete oscillation can be determined from the data in the
The Consumer Price Index (CPI) is a measure of the change in the cost of goods over time. The index was 100 for the three-year period centered on 1983. For simplicity, we will assume that the CPI was
In exercises, find an equation in slope-intercept form for each line.Through (8, -1) and (4, 3)
While shopping for an air conditioner, Manuel consulted the following table, which gives a machine’s BTUs and the square footage (ft2) that it would cool.(a) Find the equation for the least squares
Find an equation in the form y = mx + b for each line.Through (2, -10), perpendicular to a line with undefined slope
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.x-intercept -2, y-intercept 4
Assume that each situation can be expressed as a linear cost function. Find the cost function in each case.Marginal cost: $120; 700 items cost $96,500 to produce.
Find an equation in the form y = mx + b for each line.Through (-2, 5); slope = 0
The table shows the men’s and women’s outdoor world records (in seconds) in the 800-m run.Let x be the year, with x = 0 corresponding to 1900.(a) Find the equation for the least squares line for
Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through (3, -4), parallel to 4x - 2y = 9
Let the supply and demand functions for butter pecan ice cream be given bywhere p is the price in dollars and q is the number of 10-gallon tubs.(a) Graph these on the same axes.(b) Find the
Suppose that the demand and price for strawberries are related by p = D(q) = 6 - 0.25q, where p is the price (in dollars) and q is the quantity demanded (in hundreds of quarts). Find the price at
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Horizontal, through 18, 72
Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through (0, 5), perpendicular to 8x + 5y = 3
Let the supply and demand functions for sugar be given bywhere p is the price per pound and q is the quantity in thousands of pounds.(a) Graph these on the same axes.(b) Find the equilibrium quantity
An analysis similar to that of the previous exercise can be done for the 100-meter sprint, for which the winning times in the Summer Olympic Games since 1928 are listed in the table below. Let x be
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through 1-4, 62, parallel to 3x + 2y = 13
If you think a marathon is a long race, consider the Hardrock 100, a 100.5 mile running race held in southwestern Colorado. The chart which follows lists the times that the 2018 winner, Jeff
Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through (-1, 4); undefined slope
Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through (7, -6), parallel to a line with undefined slope
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through 12, -52, parallel to 2x - y = -4
Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through (3, -5), parallel to y = 4
In Exercises, find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through 13, -42, perpendicular to x + y = 4
Find an equation for each line in the form ax + by = c, where a, b, and c are integers with no factor common to all three and a ≥ 0.Through (-3, 5), perpendicular to y = -2
An interesting phenomenon occurred with the 2000 New York Yankees. The following table shows the number of base hits, triples, and home runs for those Yankees with at least 300 at-bats.(a) Find the
Suppose that the supply function for honey is p = S(q) = 0.3q + 2.7, where p is the price in dollars for an 8-oz container and q is the quantity in barrels. Suppose also that the equilibrium price is
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