B at what points is the tangent horizontal or

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t10.2Exercises
(b) At what points is the tangent horizontal or vertical?(c)At what points does the tangent have slope 1 or29.At what points on the curve,doesthe tangent line have slope ?30.Find equations of the tangents to the curvethat pass through the point31.Use the parametric equations of an ellipse,,, to find the area that it encloses.32.Find the area enclosed by the curve,andthe33.Find the area enclosed by theand the curve,34.Find the area of the region enclosed by the astroid,. (Astroids are explored in the Labo-ratory Project on page 668.)cost2 cos 2t ysint2 sin 2xrdsinyrdcosdrxacos3yasin31x2t3y14tt21x3t21y2t314, 3xacosybsin0xt22t ysty-axisx-axisx1etytt2xacos3yasin3yx0a_a_aadr?,.,..35.Find the area under one arch of the trochoid of Exercise 40 inSection 10.1 for the case.xcost2 cos 2t ysint2 sin 2xrdsinyrdcosdrxacos3yasin31x2t3y14tt21x3t21y2t314, 3xacosybsin0xt22t ysty-axisx-axisx1etytt2xacos3yasin3yx0a_a_aadrt2;Graphing calculator or computer requiredComputer algebra system required1.Homework Hints available at stewartcalculus.comCAS
676CHAPTER 1036.Letbe the region enclosed by the loop of the curve inExample 1.(a)Find the area of(b) Ifis rotated about the-axis, find the volume of theresulting solid.(c)Find the centroid ofShow that the total length of the ellipse,, isxxtetytet0t21e2sin2dwhereis the eccentricity of the ellipse, where.54.Find the total length of the astroid,where..37.,,,,40.,41–44Find the exact length of the curve.41.,42.,43.,44.,tstytst0t10t1y42t3x13t20t3y52txetet0t1ytcostxtsin0ty3 sintsin 3tx3 costcos 3,,,,,;45–46Graph the curve and find its length.,,;47.Graph the curve,and find itslength correct to four decimal places.48.Find the length of the loop of the curve.49.Use Simpson’s Rule withto estimate the length of thecurve,,3t2,.50.In Exercise 43 in Section 10.1 you were asked to derive theparametric equations,for thecurve called the witch of Maria Agnesi. Use Simpson’s Rulewithto estimate the length of the arc of this curvegiven by51–52Find the distance traveled by a particle with positionasvaries in the given time interval. Compare with the length ofthe curve.,t.,52.,t4ycostxcos2xasinab0ybcos,53.Show that the total length of the ellipse,, isxxtetytet0t21e2sin2dwhereis the eccentricity of the ellipse, where.54.Find the total length of the astroid,where,4xtstytst0t10t1y42t3x13t20t3y52txetet0t1ytcostxtsin0ty3 sintsin 3tx3 costcos 3ttt1ty3t2x,ty0t4ycostxcos2xasinab0ybcostL4ay20s1e2sin2dwhereis the eccentricity of the ellipse, where.54.Find the total length of the astroid,where,

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Term
Fall
Professor
John
Tags
Calculus, Equations, Parametric Equations, Polar Coordinates, Parametric equation, Conic section

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