 10.10.1.1: Sketch the curve by using the parametric equations to plot x 1 3t p...
 10.10.5.1: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.2.1: Find dy/dx
 10.10.6.1: Write a polar equation of a conic with the focus at the origin 21. ...
 10.10.3.1: Plot the point whose polar coordinates are given. Then find (s2 , 5...
 10.10.4.1: Find the area of the region that is bounded by the given curve r 3 ...
 10.10.1.2: Sketch the curve by using the parametric equations to plot x 1 3t p...
 10.10.5.2: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.2.2: Find dy/dx
 10.10.6.2: Write a polar equation of a conic with the focus at the origin 21. ...
 10.10.3.2: Plot the point whose polar coordinates are given. Then find (s2 , 5...
 10.10.4.2: Find the area of the region that is bounded by the given curve r 3 ...
 10.10.1.3: Sketch the curve by using the parametric equations to plot x 1 3t p...
 10.10.5.3: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.2.3: Find an equation of the tangent to the curve at the point correspon...
 10.10.6.3: Write a polar equation of a conic with the focus at the origin 21. ...
 10.10.3.3: Plot the point whose polar coordinates are given. Then find the Car...
 10.10.4.3: Find the area of the region that is bounded by the given curve r 3 ...
 10.10.1.4: Sketch the curve by using the parametric equations to plot x 1 3t p...
 10.10.5.4: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.2.4: Find an equation of the tangent to the curve at the point correspon...
 10.10.6.4: Write a polar equation of a conic with the focus at the origin 21. ...
 10.10.3.4: Plot the point whose polar coordinates are given. Then find the Car...
 10.10.4.4: Find the area of the region that is bounded by the given curve r 3 ...
 10.10.1.5: (a) Sketch the curve by using the parametric equations to plot poin...
 10.10.5.5: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.2.5: Find an equation of the tangent to the curve at the point correspon...
 10.10.6.5: Write a polar equation of a conic with the focus at the origin 21. ...
 10.10.3.5: The Cartesian coordinates of a point are given. (i) Find polar coor...
 10.10.4.5: Find the area of the shaded region.
 10.10.1.6: (a) Sketch the curve by using the parametric equations to plot poin...
 10.10.5.6: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.2.6: Find an equation of the tangent to the curve at the point correspon...
 10.10.6.6: Write a polar equation of a conic with the focus at the origin 21. ...
 10.10.3.6: The Cartesian coordinates of a point are given. (i) Find polar coor...
 10.10.4.6: Find the area of the shaded region.
 10.10.1.7: (a) Sketch the curve by using the parametric equations to plot poin...
 10.10.5.7: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.2.7: Find an equation of the tangent to the curve at the given point by ...
 10.10.6.7: Write a polar equation of a conic with the focus at the origin 21. ...
 10.10.3.7: Sketch the region in the plane consisting of points whose polar coo...
 10.10.4.7: Find the area of the shaded region.
 10.10.1.8: (a) Sketch the curve by using the parametric equations to plot poin...
 10.10.5.8: Find the vertex, focus, and directrix of the parabola and sketch it...
 10.10.2.8: Find an equation of the tangent to the curve at the given point by ...
 10.10.6.8: Write a polar equation of a conic with the focus at the origin 21. ...
 10.10.3.8: Sketch the region in the plane consisting of points whose polar coo...
 10.10.4.8: Find the area of the shaded region.
 10.10.1.9: (a) Sketch the curve by using the parametric equations to plot poin...
 10.10.5.9: Find an equation of the parabola. Then find the focus and directrix.
 10.10.2.9: Find an equation of the tangent(s) to the curve at the given point....
 10.10.6.9: (a) Find the eccentricity, (b) identify the conic, (c) give an equa...
 10.10.3.9: Sketch the region in the plane consisting of points whose polar coo...
 10.10.4.9: Sketch the curve and find the area that it encloses.
 10.10.1.10: (a) Sketch the curve by using the parametric equations to plot poin...
 10.10.5.10: Find an equation of the parabola. Then find the focus and directrix.
 10.10.2.10: Find an equation of the tangent(s) to the curve at the given point....
 10.10.6.10: (a) Find the eccentricity, (b) identify the conic, (c) give an equa...
 10.10.3.10: Sketch the region in the plane consisting of points whose polar coo...
 10.10.4.10: Sketch the curve and find the area that it encloses.
 10.10.1.11: (a) Eliminate the parameter to find a Cartesian equation of the cur...
 10.10.5.11: Find the vertices and foci of the ellipse and sketch its graph.
 10.10.2.11: Find and . For which values of is the curve concave upward?
 10.10.6.11: (a) Find the eccentricity, (b) identify the conic, (c) give an equa...
 10.10.3.11: Sketch the region in the plane consisting of points whose polar coo...
 10.10.4.11: Sketch the curve and find the area that it encloses.
 10.10.1.12: (a) Eliminate the parameter to find a Cartesian equation of the cur...
 10.10.5.12: Find the vertices and foci of the ellipse and sketch its graph.
 10.10.2.12: Find and . For which values of is the curve concave upward?
 10.10.6.12: (a) Find the eccentricity, (b) identify the conic, (c) give an equa...
 10.10.3.12: Sketch the region in the plane consisting of points whose polar coo...
 10.10.4.12: Sketch the curve and find the area that it encloses.
 10.10.1.13: (a) Eliminate the parameter to find a Cartesian equation of the cur...
 10.10.5.13: Find the vertices and foci of the ellipse and sketch its graph.
 10.10.2.13: Find and . For which values of is the curve concave upward?
 10.10.6.13: (a) Find the eccentricity, (b) identify the conic, (c) give an equa...
 10.10.3.13: Find the distance between the points with polar coordinates and .
 10.10.4.13: Sketch the curve and find the area that it encloses.
 10.10.1.14: (a) Eliminate the parameter to find a Cartesian equation of the cur...
 10.10.5.14: Find the vertices and foci of the ellipse and sketch its graph.
 10.10.2.14: Find and . For which values of is the curve concave upward?
 10.10.6.14: (a) Find the eccentricity, (b) identify the conic, (c) give an equa...
 10.10.3.14: Find a formula for the distance between the points with polarcoordi...
 10.10.4.14: Sketch the curve and find the area that it encloses.
 10.10.1.15: (a) Eliminate the parameter to find a Cartesian equation of the cur...
 10.10.5.15: Find the vertices and foci of the ellipse and sketch its graph.
 10.10.2.15: Find and . For which values of is the curve concave upward?
 10.10.6.15: (a) Find the eccentricity, (b) identify the conic, (c) give an equa...
 10.10.3.15: Identify the curve by finding a Cartesian equation for the curve.
 10.10.4.15: Graph the curve and find the area that it encloses.
 10.10.1.16: (a) Eliminate the parameter to find a Cartesian equation of the cur...
 10.10.5.16: Find the vertices and foci of the ellipse and sketch its graph.
 10.10.2.16: Find and . For which values of is the curve concave upward?
 10.10.6.16: (a) Find the eccentricity, (b) identify the conic, (c) give an equa...
 10.10.3.16: Identify the curve by finding a Cartesian equation for the curve.
 10.10.4.16: Graph the curve and find the area that it encloses.
 10.10.1.17: (a) Eliminate the parameter to find a Cartesian equation of the cur...
 10.10.5.17: Find an equation of the ellipse. Then find its foci.
 10.10.2.17: Find the points on the curve where the tangent is horizontal or ver...
 10.10.6.17: (a) Find the eccentricity and directrix of the conic and graph the ...
 10.10.3.17: Identify the curve by finding a Cartesian equation for the curve.
 10.10.4.17: Find the area of the region enclosed by one loop of the curve.
 10.10.1.18: (a) Eliminate the parameter to find a Cartesian equation of the cur...
 10.10.5.18: Find an equation of the ellipse. Then find its foci.
 10.10.2.18: Find the points on the curve where the tangent is horizontal or ver...
 10.10.6.18: Graph the conic and its directrix. Also graph the conic obtained by...
 10.10.3.18: Identify the curve by finding a Cartesian equation for the curve.
 10.10.4.18: Find the area of the region enclosed by one loop of the curve.
 10.10.1.19: Describe the motion of a particle with position as varies in the gi...
 10.10.5.19: Find the vertices, foci, and asymptotes of the hyperbola and sketch...
 10.10.2.19: Find the points on the curve where the tangent is horizontal or ver...
 10.10.6.19: Graph the conics with , , , and on a common screen. How does the va...
 10.10.3.19: Identify the curve by finding a Cartesian equation for the curve.
 10.10.4.19: Find the area of the region enclosed by one loop of the curve.
 10.10.1.20: Describe the motion of a particle with position as varies in the gi...
 10.10.5.20: Find the vertices, foci, and asymptotes of the hyperbola and sketch...
 10.10.2.20: Find the points on the curve where the tangent is horizontal or ver...
 10.10.6.20: (a) Graph the conics for and various values of . How does the value...
 10.10.3.20: Identify the curve by finding a Cartesian equation for the curve.
 10.10.4.20: Find the area of the region enclosed by one loop of the curve.
 10.10.1.21: Describe the motion of a particle with position as varies in the gi...
 10.10.5.21: Find the vertices, foci, and asymptotes of the hyperbola and sketch...
 10.10.2.21: Use a graph to estimate the coordinates of the rightmost point on t...
 10.10.6.21: Show that a conic with focus at the origin, eccentricity , and dire...
 10.10.3.21: Find a polar equation for the curve represented by the given Cartes...
 10.10.4.21: Find the area of the region enclosed by one loop of the curve.
 10.10.1.22: Describe the motion of a particle with position as varies in the gi...
 10.10.5.22: Find the vertices, foci, and asymptotes of the hyperbola and sketch...
 10.10.2.22: Use a graph to estimate the coordinates of the lowest point and the...
 10.10.6.22: Show that a conic with focus at the origin, eccentricity , and dire...
 10.10.3.22: Find a polar equation for the curve represented by the given Cartes...
 10.10.4.22: Find the area enclosed by the loop of the strophoid
 10.10.1.23: Suppose a curve is given by the parametric equations , , where the ...
 10.10.5.23: Find the vertices, foci, and asymptotes of the hyperbola and sketch...
 10.10.2.23: Graph the curve in a viewing rectangle that displays all the import...
 10.10.6.23: Show that a conic with focus at the origin, eccentricity , and dire...
 10.10.3.23: Find a polar equation for the curve represented by the given Cartes...
 10.10.4.23: Find the area of the region that lies inside the first curve and ou...
 10.10.1.24: Match the graphs of the parametric equations and in (a)(d) with the...
 10.10.5.24: Find the vertices, foci, and asymptotes of the hyperbola and sketch...
 10.10.2.24: Graph the curve in a viewing rectangle that displays all the import...
 10.10.6.24: Show that the parabolas and intersect at right angles.
 10.10.3.24: Find a polar equation for the curve represented by the given Cartes...
 10.10.4.24: Find the area of the region that lies inside the first curve and ou...
 10.10.1.25: Use the graphs of and to sketch the parametric curve , . Indicate w...
 10.10.5.25: Identify the type of conic section whose equation is given and find...
 10.10.2.25: Show that the curve , has two tangents at and find their equations....
 10.10.6.25: The orbit of Mars around the sun is an ellipse with eccentricity an...
 10.10.3.25: Find a polar equation for the curve represented by the given Cartes...
 10.10.4.25: Find the area of the region that lies inside the first curve and ou...
 10.10.1.26: Use the graphs of and to sketch the parametric curve , . Indicate w...
 10.10.5.26: Identify the type of conic section whose equation is given and find...
 10.10.2.26: Graph the curve , to discover where it crosses itself. Then find eq...
 10.10.6.26: Jupiters orbit has eccentricity and the length of the major axis is...
 10.10.3.26: Find a polar equation for the curve represented by the given Cartes...
 10.10.4.26: Find the area of the region that lies inside the first curve and ou...
 10.10.1.27: Use the graphs of and to sketch the parametric curve , . Indicate w...
 10.10.5.27: Identify the type of conic section whose equation is given and find...
 10.10.2.27: (a) Find the slope of the tangent line to the trochoid , in terms o...
 10.10.6.27: The orbit of Halleys comet, last seen in 1986 and due to return in ...
 10.10.3.27: For each of the described curves, decide if the curve would be more...
 10.10.4.27: Find the area of the region that lies inside the first curve and ou...
 10.10.1.28: Match the parametric equations with the graphs labeled IVI. Give r...
 10.10.5.28: Identify the type of conic section whose equation is given and find...
 10.10.2.28: (a) Find the slope of the tangent to the astroid , in terms of . (A...
 10.10.6.28: The HaleBopp comet, discovered in 1995, has an elliptical orbit wi...
 10.10.3.28: For each of the described curves, decide if the curve would be more...
 10.10.4.28: Find the area of the region that lies inside the first curve and ou...
 10.10.1.29: Graph the curve x y 3y 3 y 5x
 10.10.5.29: Identify the type of conic section whose equation is given and find...
 10.10.2.29: At what points on the curve , does the tangent line have slope ?
 10.10.6.29: The planet Mercury travels in an elliptical orbit with eccentricity...
 10.10.3.29: Sketch the curve with the given polar equation.
 10.10.4.29: Find the area of the region that lies inside both curves.
 10.10.1.30: Graph the curves and and find their points of intersection correct ...
 10.10.5.30: Identify the type of conic section whose equation is given and find...
 10.10.2.30: Find equations of the tangents to the curve , that pass through the...
 10.10.6.30: The distance from the planet Pluto to the sun is km at perihelion a...
 10.10.3.30: Sketch the curve with the given polar equation.
 10.10.4.30: Find the area of the region that lies inside both curves.
 10.10.1.31: (a) Show that the parametric equations 41. a b where , describe the...
 10.10.5.31: Find an equation for the conic that satisfies the given conditions.
 10.10.2.31: Use the parametric equations of an ellipse, , y b sin , , to find t...
 10.10.6.31: Using the data from Exercise 29, find the distance traveled by the ...
 10.10.3.31: Sketch the curve with the given polar equation.
 10.10.4.31: Find the area of the region that lies inside both curves.
 10.10.1.32: Use a graphing device and the result of Exercise 31(a) to draw the ...
 10.10.5.32: Find an equation for the conic that satisfies the given conditions.
 10.10.2.32: Find the area enclosed by the curve , and n 6 the .
 10.10.3.32: Sketch the curve with the given polar equation.
 10.10.4.32: Find the area of the region that lies inside both curves.
 10.10.1.33: Find parametric equations for the path of a particle that moves alo...
 10.10.5.33: Find an equation for the conic that satisfies the given conditions.
 10.10.2.33: Find the area enclosed by the and the curve
 10.10.3.33: Sketch the curve with the given polar equation.
 10.10.4.33: Find the area of the region that lies inside both curves.
 10.10.1.34: (a) Find parametric equations for the ellipse . [Hint: Modify the e...
 10.10.5.34: Find an equation for the conic that satisfies the given conditions.
 10.10.2.34: Find the area of the region enclosed by the astroid , . (Astroids a...
 10.10.3.34: Sketch the curve with the given polar equation.
 10.10.4.34: Find the area of the region that lies inside both curves.
 10.10.1.35: Use a graphing calculator or computer to reproduce the picture.
 10.10.5.35: Find an equation for the conic that satisfies the given conditions.
 10.10.2.35: Find the area under one arch of the trochoid of Exercise 40 in Sect...
 10.10.3.35: Sketch the curve with the given polar equation.
 10.10.4.35: Find the area inside the larger loop and outside the smaller loop o...
 10.10.1.36: Use a graphing calculator or computer to reproduce the picture.
 10.10.5.36: Find an equation for the conic that satisfies the given conditions.
 10.10.2.36: Let be the region enclosed by the loop of the curve in Example 1. (...
 10.10.3.36: Sketch the curve with the given polar equation.
 10.10.4.36: Find the area between a large loop and the enclosed small loop of t...
 10.10.1.37: Compare the curves represented by the parametric equations. How do ...
 10.10.5.37: Find an equation for the conic that satisfies the given conditions.
 10.10.2.37: Set up an integral that represents the length of the curve. Then us...
 10.10.3.37: Sketch the curve with the given polar equation.
 10.10.4.37: Find all points of intersection of the given curves.
 10.10.1.38: Compare the curves represented by the parametric equations. How do ...
 10.10.5.38: Find an equation for the conic that satisfies the given conditions.
 10.10.2.38: Set up an integral that represents the length of the curve. Then us...
 10.10.3.38: Sketch the curve with the given polar equation.
 10.10.4.38: Find all points of intersection of the given curves.
 10.10.1.39: Derive Equations 1 for the case 2
 10.10.5.39: Find an equation for the conic that satisfies the given conditions.
 10.10.2.39: Set up an integral that represents the length of the curve. Then us...
 10.10.3.39: Sketch the curve with the given polar equation.
 10.10.4.39: Find all points of intersection of the given curves.
 10.10.1.40: Let be a point at a distance from the center of a circle of radius ...
 10.10.5.40: Find an equation for the conic that satisfies the given conditions.
 10.10.2.40: Set up an integral that represents the length of the curve. Then us...
 10.10.3.40: Sketch the curve with the given polar equation.
 10.10.4.40: Find all points of intersection of the given curves.
 10.10.1.41: If and are fixed numbers, find parametric equations for the curve t...
 10.10.5.41: Find an equation for the conic that satisfies the given conditions.
 10.10.2.41: Find the exact length of the curve.
 10.10.3.41: Sketch the curve with the given polar equation.
 10.10.4.41: Find all points of intersection of the given curves.
 10.10.1.42: If and are fixed numbers, find parametric equations for the curve t...
 10.10.5.42: Find an equation for the conic that satisfies the given conditions.
 10.10.2.42: Find the exact length of the curve.
 10.10.3.42: Sketch the curve with the given polar equation.
 10.10.4.42: Find all points of intersection of the given curves.
 10.10.1.43: A curve, called a witch of Maria Agnesi, consists of all possible p...
 10.10.5.43: Find an equation for the conic that satisfies the given conditions.
 10.10.2.43: Find the exact length of the curve.
 10.10.3.43: Sketch the curve with the given polar equation.
 10.10.4.43: The points of intersection of the cardioid and the spiral loop , , ...
 10.10.1.44: (a) Find parametric equations for the set of all points as shown in...
 10.10.5.44: Find an equation for the conic that satisfies the given conditions.
 10.10.2.44: Find the exact length of the curve.
 10.10.3.44: Sketch the curve with the given polar equation.
 10.10.4.44: When recording live performances, sound engineers often use a micro...
 10.10.1.45: Suppose that the position of one particle at time is given by and t...
 10.10.5.45: Find an equation for the conic that satisfies the given conditions.
 10.10.2.45: Graph the curve and find its length.
 10.10.3.45: Sketch the curve with the given polar equation.
 10.10.4.45: Find the exact length of the polar curve.
 10.10.4.46: Find the exact length of the polar curve.
 10.10.1.46: If a projectile is fired with an initial velocity of meters per sec...
 10.10.5.46: Find an equation for the conic that satisfies the given conditions.
 10.10.2.46: Graph the curve and find its length.
 10.10.3.46: Sketch the curve with the given polar equation.
 10.10.4.47: Find the exact length of the polar curve.
 10.10.1.47: Investigate the family of curves defined by the parametric equation...
 10.10.5.47: Find an equation for the conic that satisfies the given conditions.
 10.10.2.47: Graph the curve and find its length.
 10.10.3.47: Sketch the curve with the given polar equation.
 10.10.4.48: Find the exact length of the polar curve.
 10.10.1.48: The swallowtail catastrophe curves are defined by the parametric eq...
 10.10.5.48: Find an equation for the conic that satisfies the given conditions.
 10.10.2.48: Find the length of the loop of the curve , y 3t . 2 x 3t t 3
 10.10.3.48: Sketch the curve with the given polar equation.
 10.10.4.49: Use a calculator to find the length of the curve correct to four de...
 10.10.1.49: The curves with equations , are called Lissajous figures. Investiga...
 10.10.5.49: The point in a lunar orbit nearest the surface of the moon is calle...
 10.10.2.49: Use Simpsons Rule with to estimate the length of the curve , , .
 10.10.3.49: The figure shows the graph of as a function of in Cartesian coordin...
 10.10.4.50: Use a calculator to find the length of the curve correct to four de...
 10.10.1.50: Investigate the family of curves defined by the parametric equation...
 10.10.5.50: A crosssection of a parabolic reflector is shown in the figure. Th...
 10.10.2.50: In Exercise 43 in Section 10.1 you were asked to derive the paramet...
 10.10.3.50: The figure shows the graph of as a function of in Cartesian coordin...
 10.10.4.51: Use a calculator to find the length of the curve correct to four de...
 10.10.5.51: In the LORAN (LOng RAnge Navigation) radio navigation system, two r...
 10.10.2.51: Find the distance traveled by a particle with position as varies in...
 10.10.3.51: Show that the polar curve (called a conchoid) has the line as a ver...
 10.10.4.52: Use a calculator to find the length of the curve correct to four de...
 10.10.5.52: Use the definition of a hyperbola to derive Equation 6 for a hyperb...
 10.10.2.52: Find the distance traveled by a particle with position as varies in...
 10.10.3.52: Show that the curve (also a conchoid) has the line as a horizontal ...
 10.10.4.53: Graph the curve and find its length.
 10.10.5.53: Show that the function defined by the upper branch of the hyperbola...
 10.10.2.53: Show that the total length of the ellipse , , , is where is the ecc...
 10.10.3.53: Show that the curve (called a cissoid of Diocles) has the line as a...
 10.10.4.54: Graph the curve and find its length.
 10.10.5.54: Find an equation for the ellipse with foci and and major axis of le...
 10.10.2.54: Find the total length of the astroid , , where a 0.
 10.10.3.54: Sketch the curve x 2 y 2 3 4x 2 y 20
 10.10.4.55: (a) Use Formula 10.2.7 to show that the area of the surface generat...
 10.10.5.55: Determine the type of curve represented by the equation in each of ...
 10.10.2.55: (a) Graph the epitrochoid with equations What parameter interval gi...
 10.10.3.55: (a) In Example 11 the graphs suggest that the limaon has an inner l...
 10.10.4.56: (a) Find a formula for the area of the surface generated by rotatin...
 10.10.5.56: (a) Show that the equation of the tangent line to the parabola at t...
 10.10.2.56: A curve called Cornus spiral is defined by the parametric equations...
 10.10.3.56: Match the polar equations with the graphs labeled IVI. Give reasons...
 10.10.5.57: Show that the tangent lines to the parabola drawn from any point on...
 10.10.2.57: Set up an integral that represents the area of the surface obtained...
 10.10.3.57: Find the slope of the tangent line to the given polar curve at the ...
 10.10.5.58: Show that if an ellipse and a hyperbola have the same foci, then th...
 10.10.2.58: Set up an integral that represents the area of the surface obtained...
 10.10.3.58: Find the slope of the tangent line to the given polar curve at the ...
 10.10.5.59: Use Simpsons Rule with to estimate the length of the ellipse .
 10.10.2.59: Find the exact area of the surface obtained by rotating the y fx gi...
 10.10.3.59: Find the slope of the tangent line to the given polar curve at the ...
 10.10.5.60: The planet Pluto travels in an elliptical orbit around the sun (at ...
 10.10.2.60: Find the exact area of the surface obtained by rotating the y fx gi...
 10.10.3.60: Find the slope of the tangent line to the given polar curve at the ...
 10.10.5.61: Find the area of the region enclosed by the hyperbola and the verti...
 10.10.2.61: Find the exact area of the surface obtained by rotating the y fx gi...
 10.10.3.61: Find the slope of the tangent line to the given polar curve at the ...
 10.10.5.62: (a) If an ellipse is rotated about its major axis, find the volume ...
 10.10.2.62: Graph the curve If this curve is rotated about the axis, find the ...
 10.10.3.62: Find the slope of the tangent line to the given polar curve at the ...
 10.10.5.63: Let be a point on the ellipse with foci and and let and be the angl...
 10.10.2.63: If the curve is rotated about the axis, use your calculator to est...
 10.10.3.63: Find the points on the given curve where the tangent line is horizo...
 10.10.5.64: Let be a point on the hyperbola with foci and and let and be the an...
 10.10.2.64: If the arc of the curve in Exercise 50 is rotated about the axis, ...
 10.10.3.64: Find the points on the given curve where the tangent line is horizo...
 10.10.2.65: Find the surface area generated by rotating the given curve about t...
 10.10.3.65: Find the points on the given curve where the tangent line is horizo...
 10.10.2.66: Find the surface area generated by rotating the given curve about t...
 10.10.3.66: Find the points on the given curve where the tangent line is horizo...
 10.10.2.67: If is continuous and for , show that the parametric curve , , , can...
 10.10.3.67: Find the points on the given curve where the tangent line is horizo...
 10.10.2.68: Use Formula 2 to derive Formula 7 from Formula 8.2.5 for the case i...
 10.10.3.68: Find the points on the given curve where the tangent line is horizo...
 10.10.2.69: The curvature at a point of a curve is defined as where is the angl...
 10.10.3.69: Show that the polar equation , where , represents a circle, and fin...
 10.10.2.70: (a) Use the formula in Exercise 69(b) to find the curvature of the ...
 10.10.3.70: Show that the curves and intersect at right angles.
 10.10.2.71: Use the formula in Exercise 69(a) to find the curvature of the cycl...
 10.10.3.71: Use a graphing device to graph the polar curve. Choose the paramete...
 10.10.2.72: (a) Show that the curvature at each point of a straight line is . (...
 10.10.3.72: Use a graphing device to graph the polar curve. Choose the paramete...
 10.10.2.73: A string is wound around a circle and then unwound whilebeing held ...
 10.10.3.73: Use a graphing device to graph the polar curve. Choose the paramete...
 10.10.2.74: A cow is tied to a silo with radius by a rope just long enough to r...
 10.10.3.74: Use a graphing device to graph the polar curve. Choose the paramete...
 10.10.3.75: Use a graphing device to graph the polar curve. Choose the paramete...
 10.10.3.76: Use a graphing device to graph the polar curve. Choose the paramete...
 10.10.3.77: How are the graphs of and related to the graph of ? In general, how...
 10.10.3.78: Use a graph to estimate the coordinate of the highest points on th...
 10.10.3.79: (a) Investigate the family of curves defined by the polar equations...
 10.10.3.80: A family of curves is given by the equations , where is a real numb...
 10.10.3.81: A family of curves has polar equations Investigate how the graph ch...
 10.10.3.82: The astronomer Giovanni Cassini (16251712) studied the family of cu...
 10.10.3.83: Let be any point (except the origin) on the curve . If is the angle...
 10.10.3.84: (a) Use Exercise 83 to show that the angle between the tangent line...
Solutions for Chapter 10: Parametric Equations and Polar Coordinates
Full solutions for Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign)  6th Edition
ISBN: 9780495011699
Solutions for Chapter 10: Parametric Equations and Polar Coordinates
Get Full SolutionsSingle Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) was written by and is associated to the ISBN: 9780495011699. Chapter 10: Parametric Equations and Polar Coordinates includes 359 full stepbystep solutions. Since 359 problems in chapter 10: Parametric Equations and Polar Coordinates have been answered, more than 17616 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign), edition: 6. This expansive textbook survival guide covers the following chapters and their solutions.

Angle of depression
The acute angle formed by the line of sight (downward) and the horizontal

Arrow
The notation PQ denoting the directed line segment with initial point P and terminal point Q.

Bounded above
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

Focus, foci
See Ellipse, Hyperbola, Parabola.

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

Future value of an annuity
The net amount of money returned from an annuity.

Inferential statistics
Using the science of statistics to make inferences about the parameters in a population from a sample.

Inverse relation (of the relation R)
A relation that consists of all ordered pairs b, a for which a, b belongs to R.

Lower bound of f
Any number b for which b < ƒ(x) for all x in the domain of ƒ

Nautical mile
Length of 1 minute of arc along the Earth’s equator.

Objective function
See Linear programming problem.

Octants
The eight regions of space determined by the coordinate planes.

Partial fraction decomposition
See Partial fractions.

Piecewisedefined function
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

Rational zeros theorem
A procedure for finding the possible rational zeros of a polynomial.

Right triangle
A triangle with a 90° angle.

Root of an equation
A solution.

Rose curve
A graph of a polar equation or r = a cos nu.

Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

Unit ratio
See Conversion factor.