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mathematics
calculus 10th edition

Calculus 10th Edition Ron Larson, Bruce H. Edwards - Solutions

Use the Vertical Line Test to determine whether is a function of x. x²-4- y = 0 43 2 1 -3-2-1 y 2F -2- 1 2 3 X
Find an equation of the line that passes through the points. Then sketch the line.(2, 8), (5, 0)
Find any intercepts and test for symmetry. Then sketch the graph of the equation.y = 2x2 + x
Find an equation of the line that passes through the points. Then sketch the line. (2,3), (0, 3)
A student who commutes 27 miles to attend college remembers, after driving a few minutes, that a term paper that is due has been forgotten. Driving faster than usual, the student returns home, picks up the paper, and once again starts toward school. Sketch a possible graph of the student’s
Find an equation of the line that passes through the points. Then sketch the line.(-3, 6), (1, 2)
Find any intercepts and test for symmetry. Then sketch the graph of the equation.y = x³ + 2
Use the Vertical Line Test to determine whether is a function of x. x² + y² = 4 -1 -1 y XA
Use the Vertical Line Test to determine whether is a function of x. y -2 x + 1, x ≤ 0 -x+ 2, x > 0 2€ -2. 2 X
Find an equation of the line that passes through the points. Then sketch the line.(6, 3), (6, 8)
Find any intercepts and test for symmetry. Then sketch the graph of the equation.y = x² - 4x
Find an equation of the line that passes through the points. Then sketch the line.(1, -2), (3, -2)
Find an equation of the line that passes through the points. Then sketch the line. (3, 3), (-))
Find any intercepts and test for symmetry. Then sketch the graph of the equation.y = x√x + 5
Find any intercepts and test for symmetry. Then sketch the graph of the equation.y = √25 - x²
Find any intercepts and test for symmetry. Then sketch the graph of the equation. y 10 x2 + 1
Show that the line with intercepts (a, 0) and (0, b) has the following equation. y a b + || 1, a 0, b 0
Find any intercepts and test for symmetry. Then sketch the graph of the equation.x = y³
Determine whether y is a function of x.x² + y² = 16
Use the result of Exercise 48 to write an equation of the line in general form.Data from in Exercise 48Show that the line with intercepts (a, 0) and (0, b) has the following equation. x-intercept: (2, 0) y-intercept: (0, 3)
Find an equation of the vertical line with x-intercept at 3.
Find any intercepts and test for symmetry. Then sketch the graph of the equation.x = y² - 4
Use the result of Exercise 48 to write an equation of the line in general form.Data from in Exercise 48Show that the line with intercepts (a, 0) and (0, b) has the following equation. Point on line: (1, 2) (a,0) (0, a) x-intercept: y-intercept: (a + 0)
Use the result of Exercise 48 to write an equation of the line in general form.Data from in Exercise 48Show that the line with intercepts (a, 0) and (0, b) has the following equation. x-intercept: (-3,0) y-intercept: (0, -2)
Determine whether y is a function of x.x² + y = 16
Find any intercepts and test for symmetry. Then sketch the graph of the equation.y = 8/x
The graph shows one of the eight basic functions and a transformation of the function. Describe the transformation. Then use your description to write an equation for the transformation. 5 43 2 -1 y 1 2 3 4 5
Determine whether y is a function of x.x2y - x2 + 4y = 0
The graph shows one of the eight basic functions and a transformation of the function. Describe the transformation. Then use your description to write an equation for the transformation. 21- 5 4 2 1 y 21 X
Find any intercepts and test for symmetry. Then sketch the graph of the equation.y = 6 - |x|
Find any intercepts and test for symmetry. Then sketch the graph of the equation.y = |6 - x|
Use the result of Exercise 48 to write an equation of the line in general form.Data from in Exercise 48Show that the line with intercepts (a, 0) and (0, b) has the following equation. Point on line: (-3,4) x-intercept: (a,0) y-intercept: (0, a) (a = 0)
The graph shows one of the eight basic functions and a transformation of the function. Describe the transformation. Then use your description to write an equation for the transformation. + -2-1 y 3- 32 1- -2+ 3 4
Use the result of Exercise 48 to write an equation of the line in general form.Data from in Exercise 48Show that the line with intercepts (a, 0) and (0, b) has the following equation. Point on line: (9, -2) x-intercept: (2a, 0) (0, a) y-intercept: (a + 0)
The graph shows one of the eight basic functions and a transformation of the function. Describe the transformation. Then use your description to write an equation for the transformation. -3 543 1 y 1 2 3
Use the result of Exercise 48 to write an equation of the line in general form.Data from in Exercise 48Show that the line with intercepts (a, 0) and (0, b) has the following equation. Point on line: (-3,-2) x-intercept: (a,0) y-intercept: (a = 0) (0, -a)
Use the graph of y = ƒ(x) to match the function with its graph.y = ƒ(x + 5) 5 C -6-5-4-3-2-1 y 2₂ -2- 1 2 3 4 5 b y = f(x) 7 + 9 10 a X
Write the general forms of the equations of the linesthrough the point (a) Parallel to the given line (b) Perpendicular to the given line Point (-7, -2) Line x = 1
Find any intercepts and test for symmetry. Then sketch the graph of the equation.y² ]- x = 9
Find any intercepts and test for symmetry. Then sketch the graph of the equation.x² + 4y² = 4
Write the general forms of the equations of the lines through the point (a) Parallel to the given line (b) Perpendicular to the given line Point Line (-1,0) y=-3
Use the graph of y = ƒ(x) to match the function with its graph.y = ƒ(x) - 5 5 C -6-5-4-3-2-1 y 2₂ -2- 1 2 3 4 5 b y = f(x) 7 + 9 10 a X
Find any intercepts and test for symmetry. Then sketch the graph of the equation.x + 3y² = 6
Use the graph of y = ƒ(x) to match the function with its graph.y = -ƒ(-x) - 2 5 C -6-5-4-3-2-1 y 2₂ -2- 1 2 3 4 5 b y = f(x) 7 + 9 10 a X
Write the general forms of the equations of the lines through the point (a) Parallel to the given line (b) Perpendicular to the given line Point (2, 1) Line 4x - 2y = 3
Write the general forms of the equations of the lines through the point (a) Parallel to the given line (b) Perpendicular to the given line Point (2,5) Line x - y = -2
Find any intercepts and test for symmetry. Then sketch the graph of the equation.3x - 4y2 = 8
Use the graph of y = ƒ(x) to match the function with its graph.y = -ƒ(x - 4) 5 C -6-5-4-3-2-1 y 2₂ -2- 1 2 3 4 5 b y = f(x) 7 + 9 10 a X
Write the general forms of the equations of the lines through the point (a) Parallel to the given line (b) Perpendicular to the given line Point (-3,2) Line x + y = 7
Use the graph of y = ƒ(x) to match the function with its graph.y = ƒ(x + 6) + 2 5 C -6-5-4-3-2-1 y 2₂ -2- 1 2 3 4 5 b y = f(x) 7 + 9 10 a X
Use the graph of y = ƒ(x) to match the function with its graph.y = ƒ(x - 1) + 3 5 C -6-5-4-3-2-1 y 2₂ -2- 1 2 3 4 5 b y = f(x) 7 + 9 10 a X
Find the points of intersection of the graphs of the equations.x + y = 84x - y = 7
Write the general forms of the equations of the lines through the point (a) Parallel to the given line (b) Perpendicular to the given line Point Line (-) 7x + 4y = 8
Find the points of intersection of the graphs of the equations.3x - 2y = -44x + 2y = - 10
Write the general forms of the equations of the lines through the point (a) Parallel to the given line (b) Perpendicular to the given line Point (4,-5) Line 3x + 4y = 7
Find the points of intersection of the graphs of the equations.x² + y = 6x + y = 4
Write the general forms of the equations of the lines through the point (a) Parallel to the given line (b) Perpendicular to the given line Point Line 5x - 3y = 0
You are given thedollar value of a product in 2012 and the rate at which thevalue of the product is expected to change during the next5 years. Write a linear equation that gives the dollar value V ofthe product in terms of the year t. (Let t = 0 represent 2010.) 2012 Value $1850 Rate $250 increase
Find the points of intersection of the graphs of the equations.x = 3 - y²y = x - 1
Find (a) ƒ(x) + g(x)(b) ƒ(x) - g(x)(c) ƒ(x) · g(x)(d) ƒ(x)/g(x) f(x) = x² + 5x +4 g(x) = x + 1
Find (a) ƒ(x) + g(x)(b) ƒ(x) - g(x)(c) ƒ(x) · g(x)(d) ƒ(x)/g(x) - f(x) = 3x - 4 g(x) = 4
Find the points of intersection of the graphs of the equations.x² + y² = 5x - y = 1
Use a graphing utility to find the points of intersection of the graphs.Check your results analytically. y = √√√x + 6 y = √√√√x² - 4x
You are given the dollar value of a product in 2012 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 0 represent 2010.) 2012
Find the points of intersection of the graphs of the equations.x² + y² = 25- 3x + y = 15
You are given the dollar value of a product in 2012 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 0 represent 2010.) 2012 Value $156 Rate $4.50
You are given the dollar value of a product in 2012 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 0 represent 2010.) 2012
Use a graphing utility to find the points of intersection of the graphs.Check your results analytically.y = x³ - 2x2 + x - 1y = -x² + 3x - 1
Use a graphing utility to find the points of intersection of the graphs.Check your results analytically.y = x4 -2x² + 1y = 1 -x²
The table shows the Gross Domestic Product, or GDP (in trillions of dollars), for selected years.(a) Use the regression capabilities of a graphing utility to find a mathematical model of the form y = at2 + bt + c for the data. In the model, y represents the GDP (in trillions of dollars) and t
Use a graphing utility to find the points of intersection of the graphs.Check your results analytically.y = -|2x - 3| + 6y = 6 - x
The table shows the numbers of cellular phone subscribers (in millions) in the United States for selected years.(a) Use the regression capabilities of a graphing utility to find a mathematical model of the form y = at² + bt + c for the data. In the model, y represents the number of subscribers (in
Determine whether the points are collinear. (-2, 1), (-1, 0), (2, -2)
Find the composite functions ƒ º g and g º ƒ. Find the domain of each composite function. Are the two composite functions equal? f(x) = 1 X g(x) = √x + 2
find the coordinates of the point of intersection of the given segments. Explain your reasoning. (-a, 0) Medians (b, c) (a,0)
Find the composite functions ƒ º g and g º ƒ. Find the domain of each composite function. Are the two composite functions equal? f(x) = 3 , g(x) = x² - 1 X
Find the coordinates of the point of intersection of the given segments. Explain your reasoning. (b, c) (-a, 0) (a,0) Perpendicular bisectors
Find the composite functions ƒ º g and g º ƒ. Find the domain of eachcomposite function. Are the two composite functions equal?ƒ(x) = x2, g(x) = √x
Find the coordinates of the point of intersection of the given segments. Explain your reasoning. (-a, 0) Altitudes (b, c) (a,0)
Determine whether the points are collinear. (Three points are collinear if they lie on the same line.)(0, 4), (7, -6), (-5, 11)
Find the composite functions ƒ º g and g º ƒ. Find the domain of each composite function. Are the two composite functions equal?ƒ(x) = x² - 1, g(x) = cos x
The resistance y in ohms of 1000 feet of solid copper wire at 77°F can be approximated by the modelwhere x is the diameter of the wire in mils (0.001 in.). Use a graphing utility to graph the model. By about what factor is the resistance changed when the diameter of the wire is doubled? y
F(x) = ƒ º g º h. Identify functions for ƒ, g, and h. F(x) = √√√√2x - 2
Find the sales necessary to break even (R = C) when the cost C of producing x units is C = 2.04x + 5600 and the revenue R from selling x units is R = 3.29x.
Show that the points of intersection in Exercises 69, 70, and 71 are collinear.Data from in Exercises 69, 70, and 71 (-a, 0) (b, c) (a,0) Perpendicular bisectors.
Find the coordinates of a second point on the graph of a function ƒ when the givenpoint is on the graph and the function is (a) Even (b) Odd 4
For what values of k does the graph of y = kx³ pass through the point?(a) (1, 4) (b) (-2, 1) (c) (0, 0) (d) (-1, -1)
A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet) of the outer ripple is given by r(t) = 0.6t, where t is the time in seconds after the pebble strikes the water. The area of the circle is given by the function A(r) = πr². Find and
For what values of k does the graph of y² = 4kx pass through the point?(a) (1, 1) (b) (2, 4)(c) (0, 0)(d) (3, 3)
A line is represented by the equation ax + by = 4.(a) When is the line parallel to the x-axis?(b) When is the line parallel to the y-axis?(c) Give values for a and b such that the line has a slope of 5/8.(d) Give values for a and b such that the line is perpendicular to y = 2/5x + 3.(e) Give values
The graphs of ƒ, g, and h areshown in the figure. Decide whether each function is even,odd, or neither. fl -4 h 4. y 4 8 X
Write an equation whose graph has the indicated property. (There may be more than one correct answer.The graph has intercepts at x = -4, x = 3, and x = 8.
F(x) = ƒ º g º h. Identify functions for ƒ, g, and h. (There are many correct answers.)F(x) = -4 sin(1 - x)
Write an equation whose graph has the indicated property. The graph has intercepts at x = -3/2, x = 4 and = 5/2
Use the graphs of the two equations to answer the questions below.(a) What are the intercepts for each equation?(b) Determine the symmetry for each equation.(c) Determine the point of intersection of the two equations. y=x² +2] +11 -4 -2 6 4 y A 2 y = x³ = x - 4 X
Find a linear equation that expresses the relationship between the temperature in degrees Celsius C and degrees Fahrenheit F. Use the fact that water freezes at 0°C (32°F) and boils at 100°C (212°F). Use the equation to convert 72°F to degrees Celsius.
(a) Prove that if a graph is symmetric with respect to the x-axis and to the y-axis, then it is symmetric with respect to the origin. Give an example to show that the converse is not true.(b) Prove that if a graph is symmetric with respect to one axis and to the origin, then it is symmetric with
Find the coordinates of a second point on the graph of a function ƒ when the given point is on the graph and the function is (a) Even (b) Odd(4, 9)
A company reimburses its sales representatives $200 per day for lodging and meals plus $0.51 per mile driven. Write a linear equation giving the daily cost C to the company in terms of x, the number of miles driven. How much does it cost the company if a sales representative drives 137 miles on a
As a salesperson, you receive a monthly salary of $2000, plus a commission of 7% of sales. You are offered a new job at $2300 per month, plus a commission of 5% of sales.(a) Write linear equations for your monthly wage W in terms of your monthly sales s for your current job and your job offer.(b)

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