CALCULUS:EARLY TRANSCENDENTALS-PACKAGE
3rd Edition
ISBN: 9780135182543
Author: Briggs
Publisher: PEARSON
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Textbook Question
Chapter 12, Problem 8RE
Parametric curves and tangent lines
a. Eliminate the parameter to obtain an equation in x and y.
b. Find the slope of the curve at the given value of t.
c. Make a sketch of the curve showing the positive orientation of the curve and the tangent line at the point corresponding to the given value of t.
8. x = 4 sin 2t, y = 3 cos 2t, for 0 ≤ t ≤ π; t = π/6
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Chapter 12 Solutions
CALCULUS:EARLY TRANSCENDENTALS-PACKAGE
Ch. 12.1 - Identify the graph generated by the parametric...Ch. 12.1 - Prob. 2QCCh. 12.1 - Describe the curve generated by x = 3 + 2t, y = 12...Ch. 12.1 - Find parametric equations for the line segment...Ch. 12.1 - Use Theorem 12.1 to find the slope of the line x =...Ch. 12.1 - Use the arc length formula to find the length of...Ch. 12.1 - Explain how a pair of parametric equations...Ch. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Give parametric equations that generate the line...
Ch. 12.1 - Find parametric equations for the complete...Ch. 12.1 - Describe the similarities between the graphs of...Ch. 12.1 - Find the slope of the parametric curve x = 2t3 +...Ch. 12.1 - Prob. 8ECh. 12.1 - Find three different pairs of parametric equations...Ch. 12.1 - Use calculus to find the arc length of the line...Ch. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.1 - Working with parametric equations Consider the...Ch. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Eliminating the parameter Eliminate the parameter...Ch. 12.1 - Eliminating the parameter Eliminate the parameter...Ch. 12.1 - Prob. 33ECh. 12.1 - Prob. 34ECh. 12.1 - Prob. 35ECh. 12.1 - Prob. 36ECh. 12.1 - Parametric equations of circles Find parametric...Ch. 12.1 - Parametric equations of circles Find parametric...Ch. 12.1 - Parametric equations of circles Find parametric...Ch. 12.1 - Parametric equations of circles Find parametric...Ch. 12.1 - Prob. 41ECh. 12.1 - Curves to parametric equations Find parametric...Ch. 12.1 - Curves to parametric equations Give a set of...Ch. 12.1 - Curves to parametric equations Give a set of...Ch. 12.1 - Prob. 45ECh. 12.1 - Curves to parametric equations Find parametric...Ch. 12.1 - Prob. 47ECh. 12.1 - Prob. 48ECh. 12.1 - Prob. 49ECh. 12.1 - Curves to parametric equations Find parametric...Ch. 12.1 - Curves to parametric equations Find parametric...Ch. 12.1 - Curves to parametric equations Find parametric...Ch. 12.1 - Circular motion Find parametric equations that...Ch. 12.1 - Circular motion Find parametric equations that...Ch. 12.1 - Circular motion Find parametric equations that...Ch. 12.1 - Circular motion Find parametric equations that...Ch. 12.1 - More parametric curves Use a graphing utility to...Ch. 12.1 - More parametric curves Use a graphing utility to...Ch. 12.1 - More parametric curves Use a graphing utility to...Ch. 12.1 - More parametric curves Use a graphing utility to...Ch. 12.1 - More parametric curves Use a graphing utility to...Ch. 12.1 - More parametric curves Use a graphing utility to...Ch. 12.1 - Implicit function graph Explain and carry out a...Ch. 12.1 - Air drop A plane traveling horizontally at 80 m/s...Ch. 12.1 - Air dropinverse problem A plane traveling...Ch. 12.1 - Prob. 66ECh. 12.1 - Prob. 67ECh. 12.1 - Derivatives Consider the following parametric...Ch. 12.1 - Derivatives Consider the following parametric...Ch. 12.1 - Prob. 70ECh. 12.1 - Derivatives Consider the following parametric...Ch. 12.1 - Prob. 72ECh. 12.1 - Tangent lines Find an equation of the line tangent...Ch. 12.1 - Tangent lines Find an equation of the line tangent...Ch. 12.1 - Tangent lines Find an equation of the line tangent...Ch. 12.1 - Tangent lines Find an equation of the line tangent...Ch. 12.1 - Slopes of tangent lines Find all the points at...Ch. 12.1 - Slopes of tangent lines Find all the points at...Ch. 12.1 - Slopes of tangent lines Find all the points at...Ch. 12.1 - Slopes of tangent lines Find all the points at...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Arc length Find the arc length of the following...Ch. 12.1 - Explain why or why not Determine whether the...Ch. 12.1 - Prob. 90ECh. 12.1 - Prob. 91ECh. 12.1 - Prob. 92ECh. 12.1 - Parametric equations of ellipses Find parametric...Ch. 12.1 - Prob. 94ECh. 12.1 - Prob. 95ECh. 12.1 - Prob. 96ECh. 12.1 - Prob. 97ECh. 12.1 - Beautiful curves Consider the family of curves...Ch. 12.1 - Prob. 99ECh. 12.1 - Prob. 100ECh. 12.1 - Prob. 101ECh. 12.1 - Lissajous curves Consider the following Lissajous...Ch. 12.1 - Area under a curve Suppose the function y = h(x)...Ch. 12.1 - Area under a curve Suppose the function y = h(x)...Ch. 12.1 - Area under a curve Suppose the function y = h(x)...Ch. 12.1 - Prob. 106ECh. 12.1 - Prob. 107ECh. 12.1 - Prob. 108ECh. 12.1 - Surfaces of revolution Let C be the curve x =...Ch. 12.1 - Prob. 110ECh. 12.1 - Surfaces of revolution Let C be the curve x =...Ch. 12.1 - Prob. 112ECh. 12.1 - Prob. 113ECh. 12.1 - Prob. 114ECh. 12.2 - Which of the following coordinates represent the...Ch. 12.2 - Draw versions of Figure 12.21 with P in the...Ch. 12.2 - Give two polar coordinate descriptions of the...Ch. 12.2 - Describe the polar curves r = 12, r = 6, and r sin...Ch. 12.2 - Prob. 5QCCh. 12.2 - Prob. 6QCCh. 12.2 - Plot the points with polar coordinates (2,6) and...Ch. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - What is the polar equation of the vertical line x...Ch. 12.2 - What is the polar equation of the horizontal line...Ch. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Graph the points with the following polar...Ch. 12.2 - Graph the points with the following polar...Ch. 12.2 - Prob. 11ECh. 12.2 - Prob. 12ECh. 12.2 - Prob. 13ECh. 12.2 - Points in polar coordinates Give two sets of polar...Ch. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Rader Airplanes are equipped with transponders...Ch. 12.2 - Prob. 24ECh. 12.2 - Converting coordinates Express the following polar...Ch. 12.2 - Converting coordinates Express the following polar...Ch. 12.2 - Converting coordinates Express the following polar...Ch. 12.2 - Converting coordinates Express the following polar...Ch. 12.2 - Converting coordinates Express the following polar...Ch. 12.2 - Converting coordinates Express the following polar...Ch. 12.2 - Converting coordinates Express the following...Ch. 12.2 - Converting coordinates Express the following...Ch. 12.2 - Converting coordinates Express the following...Ch. 12.2 - Converting coordinates Express the following...Ch. 12.2 - Converting coordinates Express the following...Ch. 12.2 - Converting coordinates Express the following...Ch. 12.2 - Prob. 37ECh. 12.2 - Prob. 38ECh. 12.2 - Prob. 39ECh. 12.2 - Prob. 40ECh. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - Prob. 45ECh. 12.2 - Prob. 46ECh. 12.2 - Prob. 47ECh. 12.2 - Prob. 48ECh. 12.2 - Cartesian-to-polar coordinates Convert the...Ch. 12.2 - Cartesian-to-polar coordinates Convert the...Ch. 12.2 - Cartesian-to-polar coordinates Convert the...Ch. 12.2 - Cartesian-to-polar coordinates Convert the...Ch. 12.2 - Prob. 53ECh. 12.2 - Prob. 54ECh. 12.2 - Prob. 55ECh. 12.2 - Prob. 56ECh. 12.2 - Graphing polar curves Graph the following...Ch. 12.2 - Graphing polar curves Graph the following...Ch. 12.2 - Prob. 59ECh. 12.2 - Prob. 60ECh. 12.2 - Graphing polar curves Graph the following...Ch. 12.2 - Graphing polar curves Graph the following...Ch. 12.2 - Graphing polar curves Graph the following...Ch. 12.2 - Graphing polar curves Graph the following...Ch. 12.2 - Prob. 65ECh. 12.2 - Prob. 66ECh. 12.2 - Prob. 67ECh. 12.2 - Prob. 68ECh. 12.2 - Using a graphing utility Use a graphing utility to...Ch. 12.2 - Using a graphing utility Use a graphing utility to...Ch. 12.2 - Prob. 71ECh. 12.2 - Using a graphing utility Use a graphing utility to...Ch. 12.2 - Using a graphing utility Use a graphing utility to...Ch. 12.2 - Using a graphing utility Use a graphing utility to...Ch. 12.2 - Prob. 75ECh. 12.2 - Prob. 76ECh. 12.2 - Prob. 77ECh. 12.2 - Prob. 78ECh. 12.2 - Circles in general Show that the polar equation...Ch. 12.2 - Prob. 80ECh. 12.2 - Prob. 81ECh. 12.2 - Prob. 82ECh. 12.2 - Prob. 83ECh. 12.2 - Equations of circles Find equations of the circles...Ch. 12.2 - Navigating A plane is 150 miles north of a radar...Ch. 12.2 - Prob. 86ECh. 12.2 - Prob. 87ECh. 12.2 - Prob. 88ECh. 12.2 - Prob. 89ECh. 12.2 - Prob. 90ECh. 12.2 - Prob. 91ECh. 12.2 - Limiting limaon Consider the family of limaons r =...Ch. 12.2 - Prob. 93ECh. 12.2 - Prob. 94ECh. 12.2 - Prob. 95ECh. 12.2 - The lemniscate family Equations of the form r2 = a...Ch. 12.2 - The rose family Equations of the form r = a sin m...Ch. 12.2 - Prob. 98ECh. 12.2 - Prob. 99ECh. 12.2 - The rose family Equations of the form r = a sin m...Ch. 12.2 - Prob. 101ECh. 12.2 - Prob. 102ECh. 12.2 - Prob. 103ECh. 12.2 - Spirals Graph the following spirals. Indicate the...Ch. 12.2 - Enhanced butterfly curve The butterfly curve of...Ch. 12.2 - Prob. 106ECh. 12.2 - Prob. 107ECh. 12.2 - Prob. 108ECh. 12.2 - Prob. 109ECh. 12.2 - Prob. 110ECh. 12.2 - Cartesian lemniscate Find the equation in...Ch. 12.3 - Verify that if y = f() sin , then y'() =f'() sin ...Ch. 12.3 - Prob. 2QCCh. 12.3 - Prob. 3QCCh. 12.3 - Prob. 4QCCh. 12.3 - Prob. 1ECh. 12.3 - Explain why the slope of the line = /2 is...Ch. 12.3 - Explain why the slope of the line tangent to the...Ch. 12.3 - What integral must be evaluated to find the area...Ch. 12.3 - What is the slope of the line = /3?Ch. 12.3 - Prob. 6ECh. 12.3 - Find the area of the shaded region.Ch. 12.3 - Prob. 8ECh. 12.3 - Explain why the point with polar coordinates (0,...Ch. 12.3 - Prob. 10ECh. 12.3 - Slopes of tangent lines Find the slope of the line...Ch. 12.3 - Slopes of tangent lines Find the slope of the line...Ch. 12.3 - Slopes of tangent lines Find the slope of the line...Ch. 12.3 - Slopes of tangent lines Find the slope of the line...Ch. 12.3 - Slopes of tangent lines Find the slope of the line...Ch. 12.3 - Slopes of tangent lines Find the slope of the line...Ch. 12.3 - Slopes of tangent lines Find the slope of the line...Ch. 12.3 - Slopes of tangent lines Find the slope of the line...Ch. 12.3 - Slopes of tangent lines Find the slope of the line...Ch. 12.3 - Slopes of tangent lines Find the slope of the line...Ch. 12.3 - Tangent line at the origin Find the polar equation...Ch. 12.3 - Prob. 22ECh. 12.3 - Multiple tangent lines at a point a. Give the...Ch. 12.3 - Multiple tangent lines at a point a. Give the...Ch. 12.3 - Horizontal and vertical tangents Find the points...Ch. 12.3 - Horizontal and vertical tangents Find the points...Ch. 12.3 - Horizontal and vertical tangents Find the points...Ch. 12.3 - Prob. 28ECh. 12.3 - Prob. 29ECh. 12.3 - Prob. 30ECh. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Intersection points and area a. Find all the...Ch. 12.3 - Intersection points and area a. Find all the...Ch. 12.3 - Intersection points and area a. Find all the...Ch. 12.3 - Intersection points and area a. Find all the...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Areas of regions Make a sketch of the region and...Ch. 12.3 - Area of plane regions Find the areas of the...Ch. 12.3 - Area of plane regions Find the areas of the...Ch. 12.3 - Area of plane regions Find the areas of the...Ch. 12.3 - Area of plane regions Find the areas of the...Ch. 12.3 - Area of polar regions Find the area of the regions...Ch. 12.3 - Area of polar regions Find the area of the regions...Ch. 12.3 - Prob. 59ECh. 12.3 - Area of polar regions Find the area of the regions...Ch. 12.3 - Two curves, three regions Determine the...Ch. 12.3 - Prob. 62ECh. 12.3 - Arc length of polar curves Find the length of the...Ch. 12.3 - Prob. 64ECh. 12.3 - Prob. 65ECh. 12.3 - Prob. 66ECh. 12.3 - Prob. 67ECh. 12.3 - Arc length of polar curves Find the length of the...Ch. 12.3 - Arc length of polar curves Find the length of the...Ch. 12.3 - Arc length of polar curves Find the length of the...Ch. 12.3 - Prob. 71ECh. 12.3 - Prob. 72ECh. 12.3 - Prob. 73ECh. 12.3 - Prob. 74ECh. 12.3 - Prob. 75ECh. 12.3 - Prob. 76ECh. 12.3 - Prob. 77ECh. 12.3 - Prob. 78ECh. 12.3 - Prob. 79ECh. 12.3 - Prob. 80ECh. 12.3 - Regions bounded by a spiral Let Rn be the region...Ch. 12.3 - Tangents and normals Let a polar curve be...Ch. 12.3 - Prob. 83ECh. 12.3 - Prob. 84ECh. 12.3 - Grazing goat problems Consider the following...Ch. 12.3 - Grazing goat problems Consider the following...Ch. 12.3 - Prob. 87ECh. 12.4 - Verify that x2+(yp)2=y+p is equivalent to x2 =...Ch. 12.4 - Prob. 2QCCh. 12.4 - In the case that the vertices and foci are on the...Ch. 12.4 - Prob. 4QCCh. 12.4 - Prob. 5QCCh. 12.4 - Prob. 6QCCh. 12.4 - Give the property that defines all parabolas.Ch. 12.4 - Prob. 2ECh. 12.4 - Give the property that defines all hyperbolas.Ch. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - What is the equation of the standard parabola with...Ch. 12.4 - Prob. 7ECh. 12.4 - Prob. 8ECh. 12.4 - Given vertices (a, 0) and eccentricity e, what are...Ch. 12.4 - Prob. 10ECh. 12.4 - What are the equations of the asymptotes of a...Ch. 12.4 - Prob. 12ECh. 12.4 - Graphing conic sections Determine whether the...Ch. 12.4 - Graphing conic sections Determine whether the...Ch. 12.4 - Graphing conic sections Determine whether the...Ch. 12.4 - Prob. 16ECh. 12.4 - Graphing conic sections Determine whether the...Ch. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Graphing conic sections Determine whether the...Ch. 12.4 - Graphing conic sections Determine whether the...Ch. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Graphing conic sections Determine whether the...Ch. 12.4 - Graphing conic sections Determine whether the...Ch. 12.4 - Prob. 27ECh. 12.4 - Graphing conic sections Determine whether the...Ch. 12.4 - Graphing conic sections Determine whether the...Ch. 12.4 - Graphing conic sections Determine whether the...Ch. 12.4 - Prob. 31ECh. 12.4 - Equations of parabolas Find an equation of the...Ch. 12.4 - Equations of parabolas Find an equation of the...Ch. 12.4 - Prob. 34ECh. 12.4 - Prob. 35ECh. 12.4 - Equations of parabolas Find an equation of the...Ch. 12.4 - From graphs to equations Write an equation of the...Ch. 12.4 - From graphs to equations Write an equation of the...Ch. 12.4 - Equations of ellipses Find an equation of the...Ch. 12.4 - Equations of ellipses Find an equation of the...Ch. 12.4 - Equations of hyperbolas Find an equation of the...Ch. 12.4 - Equations of hyperbolas Find an equation of the...Ch. 12.4 - Equations of ellipses Find an equation of the...Ch. 12.4 - Prob. 44ECh. 12.4 - Equations of hyperbolas Find an equation of the...Ch. 12.4 - Prob. 46ECh. 12.4 - Prob. 47ECh. 12.4 - Prob. 48ECh. 12.4 - From graphs to equations Write an equation of the...Ch. 12.4 - From graphs to equations Write an equation of the...Ch. 12.4 - Prob. 51ECh. 12.4 - Golden Gate Bridge Completed in 1937, San...Ch. 12.4 - Eccentricity-directrix approach Find an equation...Ch. 12.4 - Eccentricity-directrix approach Find an equation...Ch. 12.4 - Eccentricity-directrix approach Find an equation...Ch. 12.4 - Eccentricity-directrix approach Find an equation...Ch. 12.4 - Prob. 57ECh. 12.4 - Prob. 58ECh. 12.4 - Prob. 59ECh. 12.4 - Prob. 60ECh. 12.4 - Prob. 61ECh. 12.4 - Prob. 62ECh. 12.4 - Tracing hyperbolas and parabolas Graph the...Ch. 12.4 - Tracing hyperbolas and parabolas Graph the...Ch. 12.4 - Tracing hyperbolas and parabolas Graph the...Ch. 12.4 - Tracing hyperbolas and parabolas Graph the...Ch. 12.4 - Prob. 67ECh. 12.4 - Hyperbolas with a graphing utility Use a graphing...Ch. 12.4 - Tangent lines Find an equation of the tine tangent...Ch. 12.4 - Prob. 70ECh. 12.4 - Tangent lines Find an equation of the tine tangent...Ch. 12.4 - Tangent lines Find an equation of the tine tangent...Ch. 12.4 - Tangent lines for an ellipse Show that an equation...Ch. 12.4 - Prob. 74ECh. 12.4 - Prob. 75ECh. 12.4 - Prob. 76ECh. 12.4 - Another construction for a hyperbola Suppose two...Ch. 12.4 - The ellipse and the parabola Let R be the region...Ch. 12.4 - Volume of an ellipsoid Suppose that the ellipse...Ch. 12.4 - Area of a sector of a hyperbola Consider the...Ch. 12.4 - Volume of a hyperbolic cap Consider the region R...Ch. 12.4 - Prob. 82ECh. 12.4 - Prob. 83ECh. 12.4 - Prob. 84ECh. 12.4 - Prob. 85ECh. 12.4 - Prob. 86ECh. 12.4 - Prob. 87ECh. 12.4 - Prob. 88ECh. 12.4 - Shared asymptotes Suppose that two hyperbolas with...Ch. 12.4 - Focal chords A focal chord of a conic section is a...Ch. 12.4 - Focal chords A focal chord of a conic section is a...Ch. 12.4 - Focal chords A focal chord of a conic section is a...Ch. 12.4 - Prob. 93ECh. 12.4 - Prob. 94ECh. 12.4 - Confocal ellipse and hyperbola Show that an...Ch. 12.4 - Approach to asymptotes Show that the vertical...Ch. 12.4 - Prob. 97ECh. 12.4 - Prob. 98ECh. 12 - Explain why or why not Determine whether the...Ch. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Eliminating the parameter Eliminate the parameter...Ch. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Parametric curves and tangent lines a. Eliminate...Ch. 12 - Parametric curves and tangent lines a. Eliminate...Ch. 12 - Prob. 9RECh. 12 - Parametric curves a. Eliminate the parameter to...Ch. 12 - Parametric curves a. Eliminate the parameter to...Ch. 12 - Prob. 12RECh. 12 - Tangent lines Find an equation of the line tangent...Ch. 12 - Parametric descriptions Write parametric equations...Ch. 12 - Parametric description Write parametric equations...Ch. 12 - Parametric description Write parametric equations...Ch. 12 - Parametric description Write parametric equations...Ch. 12 - Parametric description Write parametric equations...Ch. 12 - Area bounded by parametric curves Find the area of...Ch. 12 - Area bounded by parametric curves Find the area of...Ch. 12 - Prob. 21RECh. 12 - Arc length Find the length of the following...Ch. 12 - Arc length Find the length of the following...Ch. 12 - Prob. 24RECh. 12 - Sets in polar coordinates Sketch the following...Ch. 12 - Prob. 26RECh. 12 - Prob. 27RECh. 12 - Prob. 28RECh. 12 - Prob. 29RECh. 12 - Prob. 30RECh. 12 - Polar curves Graph the following equations. 31. r...Ch. 12 - Prob. 32RECh. 12 - Prob. 33RECh. 12 - Prob. 34RECh. 12 - Polar conversion Write the equation...Ch. 12 - Polar conversion Consider the equation r = 4/(sin ...Ch. 12 - Prob. 37RECh. 12 - Prob. 38RECh. 12 - Prob. 39RECh. 12 - Slopes of tangent lines a. Find all points where...Ch. 12 - Slopes of tangent lines a. Find all points where...Ch. 12 - Prob. 42RECh. 12 - Prob. 43RECh. 12 - The region enclosed by all the leaves of the rose...Ch. 12 - Prob. 45RECh. 12 - The region inside the limaon r = 2 + cos and...Ch. 12 - Areas of regions Find the ares of the following...Ch. 12 - Prob. 48RECh. 12 - The area that is inside the cardioid r = 1 + cos ...Ch. 12 - Prob. 50RECh. 12 - Prob. 51RECh. 12 - Arc length of the polar curves Find the...Ch. 12 - Prob. 53RECh. 12 - Prob. 54RECh. 12 - Conic sections a. Determine whether the following...Ch. 12 - Prob. 56RECh. 12 - Prob. 57RECh. 12 - Tangent lines Find an equation of the line tangent...Ch. 12 - Tangent lines Find an equation of the line tangent...Ch. 12 - Prob. 60RECh. 12 - Prob. 61RECh. 12 - Prob. 62RECh. 12 - Prob. 63RECh. 12 - Prob. 64RECh. 12 - Prob. 65RECh. 12 - Prob. 66RECh. 12 - Eccentricity-directrix approach Find an equation...Ch. 12 - Prob. 68RECh. 12 - Prob. 69RECh. 12 - Prob. 70RECh. 12 - Prob. 71RECh. 12 - Prob. 72RECh. 12 - Prob. 73RECh. 12 - Prob. 74RECh. 12 - Lam curves The Lam curve described by...Ch. 12 - Prob. 76RE
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- 15. Please solve this and show each and every step please. PLEASE no chatgpt can I have a real person solve it please!! I am stuck. I am doing pratice problems and I do not even know where to start with this. The question is Please compute the indicated functional value.arrow_forwardUse a graph of f to estimate lim f(x) or to show that the limit does not exist. Evaluate f(x) near x = a to support your conjecture. Complete parts (a) and (b). x-a f(x)= 1 - cos (4x-4) 3(x-1)² ; a = 1 a. Use a graphing utility to graph f. Select the correct graph below.. A. W → ✓ Each graph is displayed in a [- 1,3] by [0,5] window. B. in ✓ ○ C. und ☑ Use the graphing utility to estimate lim f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x-1 ○ A. The limit appears to be approximately ☐ . (Round to the nearest tenth as needed.) B. The limit does not exist. b. Evaluate f(x) for values of x near 1 to support your conjecture. X 0.9 0.99 0.999 1.001 1.01 1.1 f(x) ○ D. + ☑ (Round to six decimal places as needed.) Does the table from the previous step support your conjecture? A. No, it does not. The function f(x) approaches a different value in the table of values than in the graph, after the approached values are rounded to the…arrow_forwardx²-19x+90 Let f(x) = . Complete parts (a) through (c) below. x-a a. For what values of a, if any, does lim f(x) equal a finite number? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. x→a+ ○ A. a= (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no values of a for which the limit equals a finite number. b. For what values of a, if any, does lim f(x) = ∞o? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. x→a+ A. (Type integers or simplified fractions) C. There are no values of a that satisfy lim f(x) = ∞. + x-a c. For what values of a, if any, does lim f(x) = -∞0? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. x→a+ A. Either a (Type integers or simplified fractions) B.arrow_forwardSketch a possible graph of a function f, together with vertical asymptotes, that satisfies all of the following conditions. f(2)=0 f(4) is undefined lim f(x)=1 X-6 lim f(x) = -∞ x-0+ lim f(x) = ∞ lim f(x) = ∞ x-4 _8arrow_forwardDetermine the following limit. lim 35w² +8w+4 w→∞ √49w+w³ 3 Select the correct choice below, and, if necessary, fill in the answer box to complete your choice. ○ A. lim W→∞ 35w² +8w+4 49w+w3 (Simplify your answer.) B. The limit does not exist and is neither ∞ nor - ∞.arrow_forwardCalculate the limit lim X-a x-a 5 using the following factorization formula where n is a positive integer and x-➡a a is a real number. x-a = (x-a) (x1+x-2a+x lim x-a X - a x-a 5 = n- + xa an-2 + an−1)arrow_forwardThe function s(t) represents the position of an object at time t moving along a line. Suppose s(1) = 116 and s(5)=228. Find the average velocity of the object over the interval of time [1,5]. The average velocity over the interval [1,5] is Vav = (Simplify your answer.)arrow_forwardFor the position function s(t) = - 16t² + 105t, complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t = 1. Time Interval Average Velocity [1,2] Complete the following table. Time Interval Average Velocity [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001] [1,2] [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001] ப (Type exact answers. Type integers or decimals.) The value of the instantaneous velocity at t = 1 is (Round to the nearest integer as needed.)arrow_forwardFind the following limit or state that it does not exist. Assume b is a fixed real number. (x-b) 40 - 3x + 3b lim x-b x-b ... Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (x-b) 40 -3x+3b A. lim x-b x-b B. The limit does not exist. (Type an exact answer.)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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