Rosen
Summer2026
Math141–Chapter10Exam
orProblems1-3,sketchagraphforeachequationbyhand(donotusecomputergraphics). Labelallcenters
F
andvertices,andclassifyascircle,ellipse,parabola,orhyperbola.
1.
2.
3.
orProblems4and5,sketchthecurverepresentedbytheparametricequation,indicatingorientation,andwrite
F
thecorrespondingCartesianequationbyeliminatingtheparameter.
4.
5.
6. Find
valueof
and
and
forthecurverepresentedbytheparametricequations
atthepoint
,
. Findthe
.
7. Writetheequationofthelinetangenttothecurve
atthepointwhere
.
ForProblems8-10,findtherectangularcoordinatesforthepointwithgivenpolarcoordinates.
8.
9.
10.
ForProblems11and12,findtwosetsofpolarcoordinatesforthepointwithgivenrectangularcoordinates.
11.
12.
ForProblems13and14,convertthepolarequationtorectangularformandsketchitsgraph.
13.
14.
15.Sketchagraphofthepolarequation
bymakingatableofvalues,andthenfindthearea
insidetheloop.
16.Setupanintegraltofindthearclengthofthecurvegivenbytheparametricequations
on
theinterval
. DONOTEVALUATETHEINTEGRAL.
17.Find
forthepolarcurve
,andthenfindtheslopeofthetangentlineatthepointwhere
. Showallworkthatledtoyourcalculations.
18.Sketchagraphofthepolarequation
. Setupanintegraltofindtheareainsideonepetal.
DONOTEVALUATETHEINTEGRAL.
0
