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Pearson eText for Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry -- Instant Access (Pearson+)
4th Edition
ISBN: 9780137399635
Author: Michael Sullivan, Michael Sullivan
Publisher: PEARSON+
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Textbook Question
Chapter F.3, Problem 62AYU
In Problems 47-72, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer.
Parallel to the line ; containing the point
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Chapter F Solutions
Pearson eText for Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry -- Instant Access (Pearson+)
Ch. F.1 - 1. On a real number line the origin is assigned...Ch. F.1 - 2. If 3 and 5 are the coordinates of two points on...Ch. F.1 - 3. If 3 and 4 are the legs of a right triangle,...Ch. F.1 - 4. Use the converse of the Pythagorean Theorem to...Ch. F.1 - 5. The area of a triangle whose base is b and...Ch. F.1 - 6. True or False Two triangles are congruent if...Ch. F.1 - 7. If ( x,y ) are the coordinates of a point P in...Ch. F.1 - 8. The coordinate axes divide the xy-plane into...Ch. F.1 - 9. If three distinct points P , Q and R all lie on...Ch. F.1 - 10. True or False The distance between two points...
Ch. F.1 - 11. True or False The point lies in quadrant IV of...Ch. F.1 - 12. True or False The midpoint of a line segment...Ch. F.1 - Multiple Choice Which of the following statements...Ch. F.1 - Choose the formula that gives the distance between...Ch. F.1 - In Problems 15 and 16, plot each point in the...Ch. F.1 - In Problems 15 and 16, plot each point in the...Ch. F.1 - 17. Plot the points ( 2,0 ),( 2,3 ),( 2,4 ),(2,1)...Ch. F.1 - 18. Plot the points ( 0,3 ),( 1,3 ),( 2,3 ),(5,3)...Ch. F.1 - In Problems 35-46, find the distance d(P1,P2)...Ch. F.1 - In Problems 35-46, find the distance d( P 1 , P 2...Ch. F.1 - In Problems 35-46, find the distance d (P1, P2)...Ch. F.1 - In Problems 35-46, find the distance d (P1, P2)...Ch. F.1 - In Problems 35-46, find the distance d (P1, P2)...Ch. F.1 - In Problems 35-46, find the distance d (P1, P2)...Ch. F.1 - Prob. 25AYUCh. F.1 - In Problem 1932 find the distance d between the...Ch. F.1 - In problems 19-32 find the distance d between the...Ch. F.1 - In Problems 35-46, find the distance d (P1, P2)...Ch. F.1 - In Problem 1932 find the distance d between the...Ch. F.1 - In Problem 1932 find the distance d between the...Ch. F.1 - In Problems 35-46, find the distance d( P 1 , P 2...Ch. F.1 - In Problems 35-46, find the distance d( P 1 , P 2...Ch. F.1 - In Problems 51-56, plot each point and form the...Ch. F.1 - In Problems 51-56, plot each point and form the...Ch. F.1 - In Problems 51-56, plot each point and form the...Ch. F.1 - In Problems 51-56, plot each point and form the...Ch. F.1 - In Problems 51-56, plot each point and form the...Ch. F.1 - In Problems 51-56, plot each point and form the...Ch. F.1 - In Problems 57-64, find the midpoint of the line...Ch. F.1 - In Problems 57-64, find the midpoint of the line...Ch. F.1 - In problems 39-48 find the midpoint of the line...Ch. F.1 - In Problems 3946 find the midpoint of the line...Ch. F.1 - In problems 39-48, find the midpoint of the line...Ch. F.1 - In Problems 57-64, find the midpoint of the line...Ch. F.1 - In problems 39-48 find the midpoint of the line...Ch. F.1 - In problems 39-48 find the midpoint of the line...Ch. F.1 - In Problems 57-64, find the midpoint of the line...Ch. F.1 - In Problems 57-64, find the midpoint of the line...Ch. F.1 - 49. Find the points having an x-coordinate of 2...Ch. F.1 - Find all points having a y-coordinate of -3 whose...Ch. F.1 - 51. Find all points on the x-axis that are 5 units...Ch. F.1 - Find all points on the y-axis that are 5 units...Ch. F.1 - 101. The medians of a triangle are the line...Ch. F.1 - 102. An equilateral triangle is one in which all...Ch. F.1 - 55. Geometry Find the midpoint of each diagonal of...Ch. F.1 - 56. Geometry Verify that the points and are the...Ch. F.1 - In Problems 103-106, find the length of each side...Ch. F.1 - In Problems 103-106, find the length of each side...Ch. F.1 - In Problems 103-106, find the length of each side...Ch. F.1 - In Problems 103-106, find the length of each side...Ch. F.1 - 109. Baseball A major league baseball “diamond” is...Ch. F.1 - 110. Little league Baseball The layout of a...Ch. F.1 - Baseball Refer to Problem 63. Overlay a...Ch. F.1 - Little league Baseball Refer to Problem 64....Ch. F.1 - Distance between Moving Objects A Ford Focus and a...Ch. F.1 - 114. Distance of a Moving Object from a Fixed...Ch. F.1 - Drafting Error When a draftsperson draws three...Ch. F.1 - Net Sales The figure illustrates how net sales of...Ch. F.1 - Poverty Threshold Poverty thresholds are...Ch. F.1 - Prob. 70AYUCh. F.1 - 71. Completing a Line Segment Plot the points A ...Ch. F.1 - 72. Write a paragraph that describes a Cartesian...Ch. F.2 - Solve: (pp. A44-A46)
Ch. F.2 - 2. Solve the equation
Ch. F.2 - 3. The points, if any, at which a graph crosses or...Ch. F.2 - Prob. 4AYUCh. F.2 - Prob. 5AYUCh. F.2 - 7. True or False To find the y-intercepts of the...Ch. F.2 - True or False The graph of an equation in two...Ch. F.2 - 9. To find the x-intercept(s), if any, of the...Ch. F.2 - 8. True or False If a graph is symmetric with...Ch. F.2 - 10. To test whether the graph of an equation is...Ch. F.2 - In Problems 1318, determine which of the given...Ch. F.2 - In Problems 1318, determine which of the given...Ch. F.2 - In Problems 1318, determine which of the given...Ch. F.2 - In Problems 1318, determine which of the given...Ch. F.2 - In Problems 1318, determine which of the given...Ch. F.2 - In Problems 1318, determine which of the given...Ch. F.2 - In Problems 11-22, find the intercepts and graph...Ch. F.2 - In Problems 11-22, find the intercepts and graph...Ch. F.2 - In Problems 11-22, find the intercepts and graph...Ch. F.2 - In Problems 11-22, find the intercepts and graph...Ch. F.2 - In Problems 11-22, find the intercepts and graph...Ch. F.2 - In Problems 11-22, find the intercepts and graph...Ch. F.2 - In Problems 11-22, find the intercepts and graph...Ch. F.2 - In Problems 11-22, find the intercepts and graph...Ch. F.2 - In Problems 11-22, find the intercepts and graph...Ch. F.2 - In Problems 11-22, find the intercepts and graph...Ch. F.2 - In Problems 11-22, find the intercepts and graph...Ch. F.2 - In Problems 11-22, find the intercepts and graph...Ch. F.2 - In Problems 23-32, plot each point. Then plot the...Ch. F.2 - In Problems 23-32, plot each point. Then plot the...Ch. F.2 - In Problems 23-32, plot each point. Then plot the...Ch. F.2 - In Problems 23-32, plot each point. Then plot the...Ch. F.2 - In Problems 23-32, plot each point. Then plot the...Ch. F.2 - In Problems 23-32, plot each point. Then plot the...Ch. F.2 - In Problems 23-32, plot each point. Then plot the...Ch. F.2 - In Problems 23-32, plot each point. Then plot the...Ch. F.2 - In Problems 23-32, plot each point. Then plot the...Ch. F.2 - In Problems 23-32, plot each point. Then plot the...Ch. F.2 - In Problems 33-44, the graph of an equation is...Ch. F.2 - In Problems 33-44, the graph of an equation is...Ch. F.2 - In Problems 33-44, the graph of an equation is...Ch. F.2 - In Problems 33-44, the graph of an equation is...Ch. F.2 - In Problems 33-44, the graph of an equation is...Ch. F.2 - In Problems 33-44, the graph of an equation is...Ch. F.2 - In Problems 33-44, the graph of an equation is...Ch. F.2 - In Problems 33-44, the graph of an equation it...Ch. F.2 - In Problems 33-44, the graph of an equation is...Ch. F.2 - In Problems 33-44, the graph of an equation is...Ch. F.2 - In Problems 33-44, the graph of an equation is...Ch. F.2 - In Problems 33-44, the graph of an equation is...Ch. F.2 - Prob. 51AYUCh. F.2 - Prob. 52AYUCh. F.2 - Prob. 53AYUCh. F.2 - Prob. 54AYUCh. F.2 - In problems 55-70, list the intercepts and test...Ch. F.2 - In Problems 49-64, list the intercepts and test...Ch. F.2 - In Problems 49-64, list the intercepts and test...Ch. F.2 - In Problems 49-64, list the intercepts and test...Ch. F.2 - In problems 55-70, list the intercepts and test...Ch. F.2 - In problems 55-70, list the intercepts and test...Ch. F.2 - In problems 55-70, list the intercepts and test...Ch. F.2 - In Problems 49-64, list the intercepts and test...Ch. F.2 - In problems 55-70, list the intercepts and test...Ch. F.2 - In problems 55-70, list the intercepts and test...Ch. F.2 - In problems 55-70, list the intercepts and test...Ch. F.2 - In problems 55-70, list the intercepts and test...Ch. F.2 - In problems 55-70, list the intercepts and test...Ch. F.2 - In Problems 49-64, list the intercepts and test...Ch. F.2 - In Problems 49-64, list the intercepts and test...Ch. F.2 - In Problems 49-64, list the intercepts and test...Ch. F.2 - In Problems 65-68, draw a quick sketch of each...Ch. F.2 - In Problems 65-68, draw a quick sketch of each...Ch. F.2 - In Problems 65-68, draw a quick sketch of each...Ch. F.2 - In Problems 65-68, draw a quick sketch of each...Ch. F.2 - If (3, b) is a point on the graph of y=4x+1, what...Ch. F.2 -
76. If (-2, b) is a point on the graph of what...Ch. F.2 - If (a,4) is a point on the graph of y= x 2 +3x ,...Ch. F.2 -
In problem 79-86, (a) find the intercepts of the...Ch. F.2 - In problem 79-86, (a) find the intercepts of the...Ch. F.2 - In problem 79-86, (a) find the intercepts of the...Ch. F.2 -
In problem 79-86, (a) find the intercepts of the...Ch. F.2 -
In problem 79-86, (a) find the intercepts of the...Ch. F.2 - In problem 79-86, (a) find the intercepts of the...Ch. F.2 - In problem 79-86, (a) find the intercepts of the...Ch. F.2 -
In problem 79-86, (a) find the intercepts of the...Ch. F.2 - Prob. 87AYUCh. F.2 - If the graph of an equation is symmetric with...Ch. F.2 - 83. If the graph of an equation is symmetric...Ch. F.2 - 84. If the graph of an equation is symmetric with...Ch. F.2 - Microphones n studios and on stages, cardioid...Ch. F.2 - Solar Energy The solar electric generating systems...Ch. F.2 - Draw a graph of an equation that contains two...Ch. F.2 - Make up an equation with the intercepts (2,0),...Ch. F.2 - 89. Draw a graph that contains the points , , ,...Ch. F.2 - Prob. 98AYUCh. F.2 - Draw a graph that contains the points ( 2,5 ) , (...Ch. F.3 - The slope of a vertical line is ______; the slope...Ch. F.3 - 2. For the line , the x-intercept is ______ and...Ch. F.3 - 3. True or False The equation is written in...Ch. F.3 - 4. True or False The slope of the line is .
Ch. F.3 - True or False The point ( 1,2 ) is on the line...Ch. F.3 - 6. Two nonvertical lines have slopes , and ,...Ch. F.3 - The lines y=2x+3andy=ax+5 are parallel if a=...Ch. F.3 - The lines y=2x1andy=ax+2 are perpendicular if...Ch. F.3 - If a line slants downward from left to right, then...Ch. F.3 - 10. Choose the formula for finding the slope m of...Ch. F.3 - 12. Choose the correct statement about the graph...Ch. F.3 - True or False Perpendicular lines have slopes that...Ch. F.3 - In Problems 13-16, (a) find the slope of the line...Ch. F.3 - In Problems 13-16, (a) find the slope of the line...Ch. F.3 - In Problems 13-16, (a) find the slope of the line...Ch. F.3 - In Problems 13-16, (a) find the slope of the line...Ch. F.3 - In Problems 17-24, plot each pair of points and...Ch. F.3 - In Problems 17-24, plot each pair of points and...Ch. F.3 - In Problems 17-24, plot each pair of points and...Ch. F.3 - In Problems 17-24, plot each pair of points and...Ch. F.3 - In Problems 17-24, plot each pair of points and...Ch. F.3 - In Problems 17-24, plot each pair of points and...Ch. F.3 - In Problems 17-24, plot each pair of points and...Ch. F.3 - In Problems 17-24, plot each pair of points and...Ch. F.3 - In problems 25-32, graph the line that contains...Ch. F.3 - In problems 25-32, graph the line that contains...Ch. F.3 - In problems 25-32, graph the line that contains...Ch. F.3 - In problems 25-32, graph the line that contains...Ch. F.3 - In problems 25-32, graph the line that contains...Ch. F.3 - In problems 25-32, graph the line that contains...Ch. F.3 - In problems 25-32, graph the line that contains...Ch. F.3 - In problems 25-32, graph the line that contains...Ch. F.3 - In problems 33-38, the slope and a point on a line...Ch. F.3 - In problems 33-38, the slope and a point on a line...Ch. F.3 - In problems 33-38, the slope and a point on a line...Ch. F.3 - In problems 33-38, the slope and a point on a line...Ch. F.3 - In problems 33-38, the slope and a point on a line...Ch. F.3 - In problems 33-38, the slope and a point on a line...Ch. F.3 - In Problems 39-46, find an equation of the line L...Ch. F.3 - In Problems 39-46, find an equation of the line L...Ch. F.3 - In Problems 39-46, find an equation of the line L...Ch. F.3 - In Problems 39-46, find an equation of the line...Ch. F.3 - In Problems 39-46, find an equation of the line L...Ch. F.3 - In Problems 39-46, find an equation of the line...Ch. F.3 - In Problems 39-46, find an equation of the line L...Ch. F.3 - In Problems 39-46, find an equation of the line L...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 5378, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 5378, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 5378, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 5378, find an equation for the line...Ch. F.3 - In Problems 5378, find an equation for the line...Ch. F.3 - In Problems 5378, find an equation for the line...Ch. F.3 - In Problems 5378, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 47-72, find an equation for the line...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 7998, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 7998, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 73-92, find the slope and y-intercept...Ch. F.3 - In Problems 93—102, (a) find the intercepts of...Ch. F.3 - In Problems 93—102, (a) find the intercepts of the...Ch. F.3 - In Problems 93—102, (a) find the intercepts of...Ch. F.3 - In Problems 93—102, (a) find the intercepts of...Ch. F.3 - In Problems 93—102, (a) find the intercepts of the...Ch. F.3 - In Problems 93—102, (a) find the intercepts of...Ch. F.3 - In Problems 93—102, (a) find the intercepts of the...Ch. F.3 - In Problems 93—102, (a) find the intercepts of...Ch. F.3 - In Problems 93—102, (a) find the intercepts of the...Ch. F.3 - In Problems 93—102, (a) find the intercepts of the...Ch. F.3 - Find an equation of the x-axis .Ch. F.3 - Find an equation of the y-axis .Ch. F.3 - In Problems 105-108, the equations of two lines...Ch. F.3 - In Problems 105-108, the equations of two lines...Ch. F.3 - In Problems 105-108, the equations of two lines...Ch. F.3 - In Problems 105-108, the equations of two lines...Ch. F.3 - In Problems 115118, write an equation of each...Ch. F.3 - In Problems 115118, write an equation of each...Ch. F.3 - In Problems 115118, write an equation of each...Ch. F.3 - In Problems 115118, write an equation of each...Ch. F.3 - Applications and Extensions
113. Geometry Use...Ch. F.3 - 114. Geometry Use slopes to show that the...Ch. F.3 - 115. Geometry Use slopes to show that the...Ch. F.3 - 116. Geometry Use slopes and the distance formula...Ch. F.3 - Geometry Truck Rentals A truck rental company...Ch. F.3 - Cost Equation The fixed cost of operating a...Ch. F.3 - Cost of driving a car, the annual fixed costs of...Ch. F.3 - Wages of a Car Salesperson Dan receives 375 per...Ch. F.3 - Electricity Rates in Florida Florida Power Light...Ch. F.3 - Natural Gas Rates in Illinoi Ameren Illinois...Ch. F.3 - Measuring Temperature The relationship between...Ch. F.3 - Measuring Temperature The Kelvin (K) scale for...Ch. F.3 - Access Ramp A wooden access ramp is being built to...Ch. F.3 - U.S. Advertising Share A report showed that...Ch. F.3 - Product Promotion A cereal company find that the...Ch. F.3 - Show that the line containing the points (a,b) and...Ch. F.3 - 129. The equation 2x - y = C defines a family of...Ch. F.3 - Prove that if two non-vertical lines have slope...Ch. F.3 - 131. Which of the following equations might have...Ch. F.3 - 132. Which of the following equations might have...Ch. F.3 - The figure shows the graph of two parallel lines....Ch. F.3 - The figure shows the graph of two perpendicular...Ch. F.3 - 135. m is for Slope The accepted symbol used to...Ch. F.3 - 136. Grade of a Road The term grade is used to...Ch. F.3 - 137. Carpentry Carpenters use the term pitch to...Ch. F.3 - Can the equation of every line be written in...Ch. F.3 - Does every line have exactly one x-intercept and...Ch. F.3 - What can you say about two lines that have equal...Ch. F.3 - What can you say about two lines with the same...Ch. F.3 - 142. If two distinct lines have the same slope but...Ch. F.3 - If two distinct lines have the same y-intercept...Ch. F.3 - 144. Which form of the equation of a line do you...Ch. F.3 - What Went Wrong? A student is asked to find the...Ch. F.4 - In Problems 1-4, find the following for each pair...Ch. F.4 - Solve the equation (x2)2=9.(pp.A66A72)Ch. F.4 - In Problems 1-4, find the following for each pair...Ch. F.4 - In Problems 1-4, find the following for each pair...Ch. F.4 - 5. List the intercepts of the following graph.Ch. F.4 - 6. Graph y= x 2 +15 using a graphing utility....Ch. F.4 - Prob. 7AYUCh. F.4 - Prob. 8AYUCh. F.4 - Prob. 9AYUCh. F.4 - Prob. 10AYUCh. F.4 - Prob. 11AYUCh. F.4 - Prob. 12AYUCh. F.4 - Prob. 13AYUCh. F.4 - Prob. 14AYUCh. F.4 - Prob. 15AYUCh. F.4 - Prob. 16AYUCh. F.4 - Prob. 17AYUCh. F.4 - Prob. 18AYUCh. F.4 - Prob. 19AYUCh. F.4 - Prob. 20AYUCh. F.4 - Prob. 21AYUCh. F.4 - Prob. 22AYUCh. F.4 - Prob. 23AYUCh. F.4 - Prob. 24AYUCh. F.4 - Prob. 25AYUCh. F.4 - Prob. 26AYUCh. F.4 - Prob. 27AYUCh. F.4 - Prob. 28AYUCh. F.4 - Prob. 29AYUCh. F.4 - Prob. 30AYUCh. F.4 - Prob. 31AYUCh. F.4 - Prob. 32AYUCh. F.4 - Prob. 33AYUCh. F.4 - Prob. 34AYUCh. F.4 - Prob. 35AYUCh. F.4 - Prob. 36AYUCh. F.4 - Prob. 37AYUCh. F.4 - Prob. 38AYUCh. F.4 - Center (2,3) and tangent to the x- axisCh. F.4 - 40. Center and tangent to the y-axis
Ch. F.4 - Prob. 41AYUCh. F.4 - Prob. 42AYUCh. F.4 - 43. Center and tangent to the y = 2
Ch. F.4 - 44. Center and tangent to the x = 1
Ch. F.4 - In Problems 45-48, match each graph with the...Ch. F.4 - (
46.
)In Problems 45-48, match each graph with...Ch. F.4 - (
In Problems 45-48, match each graph with the...Ch. F.4 - In Problems 45-48, match each graph with the...Ch. F.4 - 58. Find an equation of the line containing the...Ch. F.4 - 49. Find the area of the square in the figure.Ch. F.4 - 50. Find the area of the blue shaded region in the...Ch. F.4 - Prob. 51AYUCh. F.4 - Prob. 52AYUCh. F.4 - 53. Weather Satellites Earth is represented on a...Ch. F.4 - 54. The tangent line to a circle may be defined as...Ch. F.4 - Prob. 55AYUCh. F.4 - Use the Greek method described in problem 55 to...Ch. F.4 - Refer to Problem 54. The line x2y+4=0 is tangent...Ch. F.4 - Prob. 59AYUCh. F.4 - If the circumference of a circle is 6, what is its...Ch. F.4 - Which of the following equations might have the...Ch. F.4 - Which of the following equations might have the...Ch. F.4 - Prob. 63AYUCh. F.4 - Prob. 64AYUCh. F -
The graph below, called a scatter diagram, shows...Ch. F - ...Ch. F -
The graph below, called a scatter diagram, shows...Ch. F -
The graph below, called a scatter diagram, shows...Ch. F - ...Ch. F - Choose a location in which you would like to live....
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- 3. Consider the sequences of functions f₁: [-π, π] → R, sin(n²x) An(2) n f pointwise as (i) Find a function ƒ : [-T,π] → R such that fn n∞. Further, show that fn →f uniformly on [-π,π] as n → ∞. [20 Marks] (ii) Does the sequence of derivatives f(x) has a pointwise limit on [-7, 7]? Justify your answer. [10 Marks]arrow_forward1. (i) Give the definition of a metric on a set X. [5 Marks] (ii) Let X = {a, b, c} and let a function d : XxX → [0, ∞) be defined as d(a, a) = d(b,b) = d(c, c) 0, d(a, c) = d(c, a) 1, d(a, b) = d(b, a) = 4, d(b, c) = d(c,b) = 2. Decide whether d is a metric on X. Justify your answer. = (iii) Consider a metric space (R, d.), where = [10 Marks] 0 if x = y, d* (x, y) 5 if xy. In the metric space (R, d*), describe: (a) open ball B2(0) of radius 2 centred at 0; (b) closed ball B5(0) of radius 5 centred at 0; (c) sphere S10 (0) of radius 10 centred at 0. [5 Marks] [5 Marks] [5 Marks]arrow_forward(c) sphere S10 (0) of radius 10 centred at 0. [5 Marks] 2. Let C([a, b]) be the metric space of continuous functions on the interval [a, b] with the metric doo (f,g) = max f(x)g(x)|. xЄ[a,b] = 1x. Find: Let f(x) = 1 - x² and g(x): (i) do(f, g) in C'([0, 1]); (ii) do(f,g) in C([−1, 1]). [20 Marks] [20 Marks]arrow_forward
- Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties to find lim→-4 1 [2h (x) — h(x) + 7 f(x)] : - h(x)+7f(x) 3 O DNEarrow_forward17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t). (a) How much of the slope field can you sketch from this information? [Hint: Note that the differential equation depends only on t.] (b) What can you say about the solu- tion with y(0) = 2? (For example, can you sketch the graph of this so- lution?) y(0) = 1 y ANarrow_forward(b) Find the (instantaneous) rate of change of y at x = 5. In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the following limit. lim h→0 - f(x + h) − f(x) h The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule defining f. f(x + h) = (x + h)² - 5(x+ h) = 2xh+h2_ x² + 2xh + h² 5✔ - 5 )x - 5h Step 4 - The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x). - f(x + h) f(x) = = (x² x² + 2xh + h² - ])- = 2x + h² - 5h ])x-5h) - (x² - 5x) = ]) (2x + h - 5) Macbook Proarrow_forward
- Evaluate the integral using integration by parts. Sx² cos (9x) dxarrow_forwardLet f be defined as follows. y = f(x) = x² - 5x (a) Find the average rate of change of y with respect to x in the following intervals. from x = 4 to x = 5 from x = 4 to x = 4.5 from x = 4 to x = 4.1 (b) Find the (instantaneous) rate of change of y at x = 4. Need Help? Read It Master Itarrow_forwardVelocity of a Ball Thrown into the Air The position function of an object moving along a straight line is given by s = f(t). The average velocity of the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at t = a is the rate of change of f at a. A ball is thrown straight up with an initial velocity of 128 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 128t - 16t². (a) What is the average velocity of the ball over the following time intervals? [3,4] [3, 3.5] [3, 3.1] ft/sec ft/sec ft/sec (b) What is the instantaneous velocity at time t = 3? ft/sec (c) What is the instantaneous velocity at time t = 7? ft/sec Is the ball rising or falling at this time? O rising falling (d) When will the ball hit the ground? t = sec Need Help? Read It Watch Itarrow_forward
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